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Index

A
A New Hope: Han Solo, Star Wars: A New Hope, C3PO, Star Wars: A New Hope, Han Solo, Star Wars: A New Hope, C3PO, Star Wars: A New Hope, Wedge Antilles, Star Wars: A New Hope, Obi-Wan Kenobi, Star Wars: A New Hope, Obi-Wan Kenobi, Star Wars: A New Hope
    A-stability and A(α)-stability: Definition 11.4.2
      Adams–Bashforth formula: Paragraph
        Adams–Moulton formula: Paragraph
          Airy equation: Exercise 10.4.5
            Allen–Cahn equation: Exercise 10.1.5, Exercise 10.2.3, Example 10.5.4, Exercise 11.5.4, Example 13.4.4
              Arnoldi iteration: Algorithm 8.4.1, (8.6.2), Arnoldi iteration
                absolute stability: Definition 11.3.1
                  accuracy (relative vs. absolute): Paragraph
                    adaptivity:adjacency matrix: Definition 7.1.1, Paragraph, adjacency matrix
                      adjoint: adjoint
                        adjoint of a matrix: Paragraph, Paragraph
                          advection equation: Definition 12.1.1, Example 12.2.1, advection equation
                            advection-diffusion equation: Paragraph, Paragraph, Example 13.2.3, Example 13.4.3
                              algorithm: Paragraph, algorithm
                                aliasing: Exercise 9.5.2
                                  argmin: Definition 3.1.1
                                    asymptotic: asymptotic
                                      asymptotic notation: Definition 2.5.1
                                        B
                                        Bauer–Fike theorem: Paragraph
                                          Bessel equation: Exercise 10.1.1, Exercise 10.4.4
                                            Bessel function: Example 4.1.1
                                              Black–Scholes equation: Paragraph
                                                Broyden update: Paragraph
                                                  Burgers equation: Exercise 12.1.3
                                                    backward difference: Definition 5.4.2
                                                      backward differentiation formula for IVPs: Paragraph
                                                        backward error: Definition 1.4.1, Observation 4.1.1, Paragraph, backward errorbackward substitution: Paragraph, backward substitution
                                                          banded matrix: Paragraph, Note
                                                            bandwidth: bandwidth
                                                              bandwidth of a matrix: Definition 2.9.1
                                                                barycentric interpolation formula: Theorem 9.2.1, barycentric interpolation formula
                                                                  barycentric weights: Definition 9.2.1
                                                                    beam equation: Exercise 12.4.6
                                                                      big-O: big-O
                                                                        boundary conditions:boundary-value problem: boundary-value problem
                                                                          C
                                                                          C3PO: C3PO, Star Wars: A New Hope, C3PO, Star Wars: A New Hope
                                                                            CFL condition: Theorem 12.2.1
                                                                              Carrier equation: Exercise 10.1.1, Exercise 10.5.7
                                                                                Chebyshev equation: Exercise 10.1.2
                                                                                  Chebyshev points:Chebyshev polynomials: Definition 9.4.4
                                                                                    Cholesky factorization: Theorem 2.9.2, Cholesky factorization
                                                                                      Clenshaw–Curtis integration: Paragraph
                                                                                        Crank–Nicolson method: Exercise 11.2.3
                                                                                          cardinal function: Definition 5.1.2, Paragraph, Paragraph, Paragraph, cardinal function
                                                                                            centered difference: Definition 5.4.2
                                                                                              characteristic polynomial: Paragraph
                                                                                                collocation: Paragraph, collocation
                                                                                                  condition number: condition numberconjugate gradients: Definition 8.6.1
                                                                                                    conservation law: Paragraph
                                                                                                      contraction mapping: Paragraph
                                                                                                        convergence rate:cubic spline: Definition 5.3.1, cubic spline
                                                                                                          D
                                                                                                          D'Alembert's solution: Exercise 12.4.3
                                                                                                            Dahlquist theorems: Theorem 6.8.2, Theorem 6.8.3, Theorem 11.4.1
                                                                                                              Dirichlet boundary condition: Definition 10.1.2, Paragraph
                                                                                                                Dirichlet boundary conditions: Paragraph
                                                                                                                  Dirichlet condition: Dirichlet condition
                                                                                                                    data fitting: Paragraphdiagonal matrix: Paragraph, Definition 7.2.3, Definition 7.3.1
                                                                                                                      diagonalizable matrix: Definition 7.2.3, diagonalizable matrix
                                                                                                                        differentiation matrix: Definition 10.3.1, Definition 10.3.2, Definition 10.3.3, Definition 10.3.4, Paragraph, Paragraph, differentiation matrix
                                                                                                                          diffusion equation: See heat equation
                                                                                                                            dimension reduction: Paragraph, Paragraph
                                                                                                                              divide and conquer: Section 5.7.2
                                                                                                                                domain of dependence: Definition 12.2.1
                                                                                                                                  dominant eigenvalue: dominant eigenvalue
                                                                                                                                    double exponential transformation: Paragraph
                                                                                                                                      double precision: double precision
                                                                                                                                        E
                                                                                                                                        Euler's method: Paragraph, Paragraph
                                                                                                                                          Euler–Maclaurin formula: Paragraph
                                                                                                                                            Euler’s method: Euler’s method
                                                                                                                                              eigenvalue: Definition 7.2.1, Comment, eigenvalueeigenvalue decomposition: Definition 7.2.3, Paragraph, Paragraph, eigenvalue decomposition
                                                                                                                                                eigenvector: Definition 7.2.1, eigenvector
                                                                                                                                                  elliptic PDE: Paragraph
                                                                                                                                                    evolutionary PDE: Paragraph, evolutionary PDE
                                                                                                                                                      extrapolation: Paragraph, extrapolation
                                                                                                                                                        F
                                                                                                                                                        FFT (fast Fourier transform): Paragraph
                                                                                                                                                          Fisher equation: Exercise 11.5.5
                                                                                                                                                            Francis QR iteration: Paragraph
                                                                                                                                                              Frobenius norm: Frobenius norm
                                                                                                                                                                field of values: Exercise 7.4.4
                                                                                                                                                                  fill-in of sparse matrices: Paragraph
                                                                                                                                                                    finite differences: Definition 5.4.1, Paragraph, Paragraph, finite differencesfinite element method: Paragraph
                                                                                                                                                                      finite element method (FEM): finite element method (FEM)
                                                                                                                                                                        finite-difference formula:fixed point problem: fixed point problem
                                                                                                                                                                          fixed-point iteration: Algorithm 4.2.1, fixed-point iteration
                                                                                                                                                                            fixed-point problem: Definition 4.2.1
                                                                                                                                                                              floating-point numbers: Definition 1.1.1, Paragraph, floating-point numbers
                                                                                                                                                                                flops: Paragraph, flops
                                                                                                                                                                                  forward difference: Definition 5.4.2
                                                                                                                                                                                    forward substitution: Paragraph, forward substitution
                                                                                                                                                                                      G
                                                                                                                                                                                      GMRES: Algorithm 8.5.1, GMRESGalerkin conditions: (10.6.10)
                                                                                                                                                                                        Gaussian elimination: Paragraph, Gaussian elimination
                                                                                                                                                                                          Gaussian integration: Paragraph
                                                                                                                                                                                            Gauss–Newton method: Algorithm 4.7.1, Gauss–Newton method
                                                                                                                                                                                              Gibbs phenomenon: Exercise 9.5.5
                                                                                                                                                                                                Gram matrix: Definition 9.4.2
                                                                                                                                                                                                  Gregory integration formula: Exercise 5.6.2
                                                                                                                                                                                                    generating polynomials: Paragraph, generating polynomials
                                                                                                                                                                                                      global error: Definition 6.2.3, global error
                                                                                                                                                                                                        graph: Definition 7.1.1, graph
                                                                                                                                                                                                          H
                                                                                                                                                                                                          Han Solo: Han Solo, Star Wars: A New Hope, Han Solo, The Empire Strikes Back, Han Solo, Star Wars: A New Hope, Han Solo, The Empire Strikes Back
                                                                                                                                                                                                            Helmholtz equation: Exercise 8.1.6, Exercise 8.6.6
                                                                                                                                                                                                              Hermite equation: Exercise 10.1.2
                                                                                                                                                                                                                Horner's algorithm: Example 1.3.1
                                                                                                                                                                                                                  Householder reflector: Definition 3.4.1
                                                                                                                                                                                                                    hat functions: Paragraph, hat functions
                                                                                                                                                                                                                      heat equation: Definition 11.1.1, Paragraph, Example 13.2.2, heat equation
                                                                                                                                                                                                                        hermitian: hermitian
                                                                                                                                                                                                                          hermitian matrix: Paragraph, Paragraph, Theorem 7.3.2
                                                                                                                                                                                                                            hermitian positive definite matrix: hermitian positive definite matrix See symmetric positive definite matrix
                                                                                                                                                                                                                              homogeneous boundary condition: Definition 10.1.2, Paragraph, homogeneous boundary condition
                                                                                                                                                                                                                                hyperbolic PDE: Definition 12.1.1
                                                                                                                                                                                                                                  I
                                                                                                                                                                                                                                  IEEE 754: Paragraph, Exercise 1.1.4
                                                                                                                                                                                                                                    identity matrix: Paragraph, Paragraph, identity matrix
                                                                                                                                                                                                                                      ill-conditioned: ill-conditioned
                                                                                                                                                                                                                                        image (as a matrix): Paragraph, Example 7.5.1, Paragraph
                                                                                                                                                                                                                                          implicit: implicit
                                                                                                                                                                                                                                            implicit IVP solver: Definition 6.6.1, Paragraph
                                                                                                                                                                                                                                              improper integral: Exercise 5.7.3, Paragraph
                                                                                                                                                                                                                                                induced matrix norm: induced matrix norm
                                                                                                                                                                                                                                                  initial-boundary-value problem: Paragraph
                                                                                                                                                                                                                                                    initial-value problem: Definition 6.1.1, initial-value probleminner product: Paragraph, inner productinner product space: Definition 9.4.1
                                                                                                                                                                                                                                                      interpolation: Definition 5.1.1, Paragraph, interpolationinverse iteration: Algorithm 8.3.1, inverse iteration
                                                                                                                                                                                                                                                        invertible matrix: Paragraph
                                                                                                                                                                                                                                                          J
                                                                                                                                                                                                                                                          Jacobian matrix: Paragraph, Paragraph, Paragraph, Jacobian matrix
                                                                                                                                                                                                                                                            Julia:
                                                                                                                                                                                                                                                            K
                                                                                                                                                                                                                                                            Kronecker product: Definition 13.3.2, Kronecker product
                                                                                                                                                                                                                                                              Krylov matrix: Definition 8.4.1
                                                                                                                                                                                                                                                                Krylov subspace: Definition 8.4.1, Krylov subspace
                                                                                                                                                                                                                                                                  Kuramoto–Sivashinsky equation: Exercise 12.1.4
                                                                                                                                                                                                                                                                    L
                                                                                                                                                                                                                                                                    LU factorization: Definition 2.4.1, Paragraph, Paragraph, LU factorizationLagrange formula: Lagrange formula
                                                                                                                                                                                                                                                                      Lagrange interpolation formula: Theorem 9.1.2
                                                                                                                                                                                                                                                                        Lagrange polynomial: Definition 9.1.1
                                                                                                                                                                                                                                                                          Laguerre equation: Exercise 10.1.2
                                                                                                                                                                                                                                                                            Lanczos iteration: Paragraph, (8.6.2), Lanczos iteration
                                                                                                                                                                                                                                                                              Laplace equation: Paragraph, Laplace equation
                                                                                                                                                                                                                                                                                Legendre equation: Exercise 10.1.2
                                                                                                                                                                                                                                                                                  Legendre polynomials: Definition 9.4.3
                                                                                                                                                                                                                                                                                    Levenberg's method: Algorithm 4.6.2
                                                                                                                                                                                                                                                                                      Lipschitz condition: Definition 4.2.3
                                                                                                                                                                                                                                                                                        Luke Skywalker: Luke Skywalker, Return of the Jedi
                                                                                                                                                                                                                                                                                          linear combination: Paragraph
                                                                                                                                                                                                                                                                                            linear convergence: Definition 4.2.2, linear convergence
                                                                                                                                                                                                                                                                                              linear least-squares problem: Paragraph, Paragraph, Paragraph, linear least-squares problem
                                                                                                                                                                                                                                                                                                linearization of an ODE: Definition 11.4.1
                                                                                                                                                                                                                                                                                                  local truncation error: local truncation error
                                                                                                                                                                                                                                                                                                    logistic equation: Paragraph
                                                                                                                                                                                                                                                                                                      M
                                                                                                                                                                                                                                                                                                      MATLAB:MINRES: Paragraph
                                                                                                                                                                                                                                                                                                        Maxwell's equations: Paragraph
                                                                                                                                                                                                                                                                                                          machine epsilon: Definition 1.1.2, Paragraph, Paragraph, machine epsilonmantissa: See significand
                                                                                                                                                                                                                                                                                                            mass matrix: Paragraph
                                                                                                                                                                                                                                                                                                              matrix condition number: matrix condition number
                                                                                                                                                                                                                                                                                                                matrix factorization: Theorem 7.3.2matrix inverse: Paragraph, Paragraph
                                                                                                                                                                                                                                                                                                                  matrix multiplication: Paragraph
                                                                                                                                                                                                                                                                                                                    method of lines: Paragraph, Paragraph, Paragraph, Paragraph, method of lines
                                                                                                                                                                                                                                                                                                                      multistep: multistep
                                                                                                                                                                                                                                                                                                                        multistep method: Definition 6.6.1, Paragraph
                                                                                                                                                                                                                                                                                                                        N
                                                                                                                                                                                                                                                                                                                        NaN: Paragraph
                                                                                                                                                                                                                                                                                                                          Neumann boundary condition: Definition 10.1.2, Paragraph
                                                                                                                                                                                                                                                                                                                            Neumann condition: Neumann condition
                                                                                                                                                                                                                                                                                                                              Newton's method: Algorithm 4.3.1, Paragraph, ParagraphNewton’s method: Newton’s method
                                                                                                                                                                                                                                                                                                                                nodes: nodes
                                                                                                                                                                                                                                                                                                                                  nonlinear least squares: Definition 4.7.1
                                                                                                                                                                                                                                                                                                                                    nonlinear least-squares problem: nonlinear least-squares problem
                                                                                                                                                                                                                                                                                                                                      norm: normnormal equations: Theorem 3.2.1, Theorem 3.2.2, Paragraph, normal equations
                                                                                                                                                                                                                                                                                                                                        normal matrix: Definition 7.2.5, normal matrix
                                                                                                                                                                                                                                                                                                                                          numerical domain of dependence: Paragraph
                                                                                                                                                                                                                                                                                                                                            numerical integration: Paragraph, Paragraph, numerical integration
                                                                                                                                                                                                                                                                                                                                              O
                                                                                                                                                                                                                                                                                                                                              ONC matrix: Definition 3.3.2, Paragraph, ONC matrix
                                                                                                                                                                                                                                                                                                                                                Obi-Wan Kenobi: Obi-Wan Kenobi, Star Wars: A New Hope, Obi-Wan Kenobi, Star Wars: A New Hope
                                                                                                                                                                                                                                                                                                                                                  Oregonator: Example 11.4.1
                                                                                                                                                                                                                                                                                                                                                    one-step IVP method: one-step IVP method
                                                                                                                                                                                                                                                                                                                                                      order of accuracy: Paragraph, order of accuracyorthogonal functions: Definition 9.4.1
                                                                                                                                                                                                                                                                                                                                                        orthogonal matrix: Paragraph, Paragraph, Definition 3.4.1, Definition 7.2.2, orthogonal matrix
                                                                                                                                                                                                                                                                                                                                                          orthogonal polynomials: Paragraph, orthogonal polynomials
                                                                                                                                                                                                                                                                                                                                                            orthogonal vectors: Paragraph, orthogonal vectors
                                                                                                                                                                                                                                                                                                                                                              orthonormal vectors: Paragraph, orthonormal vectors
                                                                                                                                                                                                                                                                                                                                                                outer product: Paragraph, Paragraph, Paragraph, outer product
                                                                                                                                                                                                                                                                                                                                                                  overdetermined: overdetermined
                                                                                                                                                                                                                                                                                                                                                                    P
                                                                                                                                                                                                                                                                                                                                                                    PLU factorization: Definition 2.6.1, PLU factorization
                                                                                                                                                                                                                                                                                                                                                                      Poisson equation: Paragraph
                                                                                                                                                                                                                                                                                                                                                                        Python:parabolic PDE: Definition 11.1.1
                                                                                                                                                                                                                                                                                                                                                                          parameter continuation: Paragraph
                                                                                                                                                                                                                                                                                                                                                                            pendulum: Exercise 10.2.2
                                                                                                                                                                                                                                                                                                                                                                              piecewise linear: piecewise linear
                                                                                                                                                                                                                                                                                                                                                                                piecewise linear interpolant: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                  pivoting: Paragraph, Paragraph, Theorem 2.9.2
                                                                                                                                                                                                                                                                                                                                                                                    power iteration: Algorithm 8.2.1, power iteration
                                                                                                                                                                                                                                                                                                                                                                                      preconditioning: Definition 8.8.1, preconditioning
                                                                                                                                                                                                                                                                                                                                                                                        predator–prey model: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                          pseudoinverse: Definition 3.2.2, pseudoinverse
                                                                                                                                                                                                                                                                                                                                                                                            Q
                                                                                                                                                                                                                                                                                                                                                                                            QR factorization: QR factorization
                                                                                                                                                                                                                                                                                                                                                                                              quadratic convergence: Definition 4.3.1, quadratic convergence
                                                                                                                                                                                                                                                                                                                                                                                                quadrature: See numerical integration
                                                                                                                                                                                                                                                                                                                                                                                                  quasi-Newton method: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                    quasi-Newton methods: quasi-Newton methods
                                                                                                                                                                                                                                                                                                                                                                                                      quasimatrix: Definition 9.4.2, quasimatrix
                                                                                                                                                                                                                                                                                                                                                                                                        R
                                                                                                                                                                                                                                                                                                                                                                                                        Rayleigh quotient: Paragraph, Rayleigh quotient
                                                                                                                                                                                                                                                                                                                                                                                                          Return of the Jedi: Luke Skywalker, Return of the Jedi
                                                                                                                                                                                                                                                                                                                                                                                                            Robin boundary condition: Definition 10.1.2
                                                                                                                                                                                                                                                                                                                                                                                                              Runge phenomenon: Paragraph, Runge phenomenon
                                                                                                                                                                                                                                                                                                                                                                                                                Runge–Kutta: Runge–Kutta
                                                                                                                                                                                                                                                                                                                                                                                                                  Runge–Kutta method: Paragraph, Paragraph, Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                    reduced QR factorization: reduced QR factorization
                                                                                                                                                                                                                                                                                                                                                                                                                      reduced SVD: reduced SVD
                                                                                                                                                                                                                                                                                                                                                                                                                        residual: Paragraph, Paragraph, Paragraph, Paragraph, Paragraph, residualrestarting: restarting
                                                                                                                                                                                                                                                                                                                                                                                                                          rootfinding problem: Definition 4.1.1, Paragraph, (11.5.6), rootfinding problemroots:row pivoting: row pivoting
                                                                                                                                                                                                                                                                                                                                                                                                                            S
                                                                                                                                                                                                                                                                                                                                                                                                                            SPD matrix: See symmetric positive definite matrix
                                                                                                                                                                                                                                                                                                                                                                                                                              SVD: See singular value decomposition
                                                                                                                                                                                                                                                                                                                                                                                                                                Simpson's formula: Paragraph, Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                  Sylvester equation: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                    secant method: Algorithm 4.4.1, secant method
                                                                                                                                                                                                                                                                                                                                                                                                                                      semidiscretization:shifted inverse iteration: See inverse iteration
                                                                                                                                                                                                                                                                                                                                                                                                                                        shock wave: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                          shooting: shooting
                                                                                                                                                                                                                                                                                                                                                                                                                                            significand: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                              significant digits: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                similar matrices: similar matrices
                                                                                                                                                                                                                                                                                                                                                                                                                                                  similarity transformation: Paragraph, similarity transformation
                                                                                                                                                                                                                                                                                                                                                                                                                                                    simple root: simple root
                                                                                                                                                                                                                                                                                                                                                                                                                                                      sine integral function: Exercise 5.7.5
                                                                                                                                                                                                                                                                                                                                                                                                                                                        sine–Gordon equation: Exercise 12.4.5
                                                                                                                                                                                                                                                                                                                                                                                                                                                          singular matrix: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                            singular value decomposition: Definition 7.3.1, Paragraph, singular value decompositionsoap film: Exercise 13.4.2
                                                                                                                                                                                                                                                                                                                                                                                                                                                              sparse matrix: Paragraph, Paragraph, Paragraph, Paragraph, Note, sparse matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                spectral convergence: spectral convergence
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  spline (cubic spline): Definition 5.3.1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    stability: Paragraph, Paragraphstability region: Definition 11.3.2, stability region
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      steepest descent: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        step size: step size
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          stiff differential equation: Paragraph, Paragraph, Example 6.7.2, stiff differential equation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            stiffness matrix: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              subtractive cancellation: Paragraph, Paragraph, Paragraph, Paragraph, Paragraph, subtractive cancellation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                superlinear convergence: Paragraph, superlinear convergence
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  symmetric matrix: Paragraph, Definition 2.9.2, Paragraph, Paragraph, symmetric matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    symmetric positive definite matrix: Definition 2.9.3, Paragraph, Definition 8.6.1, symmetric positive definite matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      T
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      The Empire Strikes Back: Yoda, The Empire Strikes Back, Han Solo, The Empire Strikes Back, Yoda, The Empire Strikes Back, Yoda, The Empire Strikes Back, Han Solo, The Empire Strikes Back
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        tensor-product domain: Note, tensor-product domain
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          tensor-product grid: Section 13.1.1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            thin QR factorization: thin QR factorization
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              thin SVD: thin SVD
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                transpose: Paragraph, Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  trapezoid formula: trapezoid formulatriangular matrix: Paragraph, Paragraph, triangular matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    tridiagonal matrix: Definition 2.9.1, tridiagonal matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      trigonometric interpolation: trigonometric interpolation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        trigonometric polynomial: Definition 9.5.1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          truncation error: truncation error
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          U
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          unit lower triangular matrix: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            unit roundoff: Definition 1.1.2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              unit triangular matrix: unit triangular matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                unit vector: Paragraph, unit vector
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  unitary matrix: Definition 7.2.2, Definition 7.2.5, Definition 7.3.1, Theorem 7.4.2, unitary matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    unstable: unstable
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      unvec: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        upper Hessenberg matrix: Definition 8.4.2, upper Hessenberg matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          upwind direction: Definition 12.2.3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            V
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Vandermonde matrix: Definition 2.1.2, Paragraph, Vandermonde matrix
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              van der Pol equation: Exercise 11.4.5
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                vec: Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  W
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Wedge Antilles: Wedge Antilles, Star Wars: A New Hope
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    wave equation: Definition 12.4.1, Paragraph
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      weak solution: Definition 10.6.1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        weights: weights
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Y
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Yoda: Yoda, The Empire Strikes Back, Yoda, The Empire Strikes Back, Yoda, The Empire Strikes Back
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Z
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            zero-stability: Definition 6.8.1, zero-stability