- 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
in IVP solver: Paragraph, Section 6.7.4
in integration: Section 5.7.2
- B
- Bauer–Fike theorem: Paragraph
in a linear system: Paragraph
inflow: Paragraph
numerical implementation of: Paragraph, Paragraph, Paragraph, Paragraph
periodic: Paragraph
- C
- C3PO: C3PO, Star Wars: A New Hope, C3PO, Star Wars: A New Hope
of a matrix: Paragraph, Definition 3.2.3, Paragraph, Notebook-code, Notebook-code, Notebook-code
of a scalar function: Definition 1.2.1
of eigenvalues: Paragraph
of elementary functions: Paragraph
of initial-value problems: Paragraph
of interpolation: Theorem 5.1.1, Theorem 5.2.1
of linear least squares: Definition 3.2.3
of linear system: Paragraph
of normal equations: Paragraph
of rootfinding: Theorem 4.1.1
algebraic: Definition 5.2.2
linear: Definition 4.2.3, Paragraph, Paragraph, Paragraph
quadratic: Definition 4.3.2, Paragraph
superlinear: Paragraph
- D
- D'Alembert's solution: Exercise 12.4.3
vector-valued function: Definition 4.5.2
- E
- Euler's method: Paragraph, Paragraph
- F
- FFT (fast Fourier transform): Paragraph
first derivative: Definition 10.3.2
second derivative: Definition 10.3.3
- G
- GMRES: Algorithm 8.5.1, GMRES
preconditioning in: Definition 8.8.1
relationship to MINRES: Paragraph
restarting: Section 8.5.3
- H
- HPD matrix: HPD matrix
- I
- IEEE 754: Paragraph, Exercise 1.1.4
one-step method for: Definition 6.2.2
of functions: Definition 9.4.1
of vectors: Paragraph
by piecewise linear polynomials: Paragraph
by piecewise polynomials: Paragraph, Paragraph, Paragraph, Paragraph
by polynomials: Paragraph, Paragraph, Paragraph, Paragraph, Paragraph
by trigonometric polynomials: Paragraph
- J
- Jacobian matrix: Definition 4.5.2, Paragraph, Paragraph, Jacobian matrix
+=: Paragraph
.+: Paragraph
.-: Paragraph
@.: Paragraph
@animate: Notebook-code, Paragraph
Boolean indexing: Paragraph
DiagonalPreconditioner: Paragraph
FNC: Paragraph
I: Paragraph
LinearMap: Paragraph
NaN: Paragraph
ODEProblem: Notebook-code
Pair: Paragraph
Rational: Paragraph
Spline1D: Paragraph
\!: Paragraph
annotate!: Notebook-code, Notebook-code
anonymous functions: Paragraph
break: Algorithm 4.3.1
cg: Paragraph
cholesky: Paragraph
collect: Paragraph
comprehension: Paragraph
destructuring: Paragraph
eachindex: Algorithm 9.5.1
eigen: Paragraph
eigs: Paragraph
eigvals: Paragraph
eltype: Paragraph
end: Paragraph
fft: Paragraph
fill: Paragraph
for: About the code, Paragraph
functions: Paragraph
gmres: Paragraph
graphplot: Paragraph
ilu: Paragraph
isinf: Algorithm 9.2.1
isodd: Algorithm 9.5.1
keyword function arguments: Algorithm 4.3.1, Algorithm 5.7.1, Notebook-code
kron: Paragraph
length: About the code, Paragraph
maximum: Paragraph
minimum: Paragraph
minres: Notebook-code
namespace: Paragraph
nnz: Paragraph
norm: Paragraph
opnorm: Paragraph
plotting functions: Paragraph
push!: Notebook-code, Notebook-code
push\!: Paragraph
quadgk: Paragraph
rank: Paragraph
reshape: Paragraph
return: Paragraph
scatter: Paragraph
scientific notation: Paragraph
size: Paragraph
solve: Notebook-code
sortby: Paragraph
sortperm: Paragraph
sparse: Paragraph
spdiagm: Paragraph
splatting: Paragraph
sprandsym: Paragraph
string interpolation: Paragraph
subplots: Paragraph
sum: Paragraph, About the code
summarysize: Paragraph
svd: Paragraph
svdvals: Paragraph
ternary operator: Algorithm 9.5.1
transpose: Paragraph
using: Paragraph
vec operation: Paragraph
÷: Paragraph
- K
- Kronecker product: Definition 13.3.2, Kronecker product
- L
- LU factorization: Definition 2.4.2, Paragraph, Paragraph, LU factorization
incomplete: Paragraph
- M
- MATLAB:
Boolean indexing: Paragraph
NaN: Paragraph
\~: Paragraph
animation: Notebook-code, Paragraph
anonymous functions: Paragraph
broadcasting: Paragraph
chol: Paragraph
cond: Paragraph
diagm: Paragraph
eig: Paragraph
eigs: Paragraph
end: Paragraph
fill: Paragraph
format: Tip
fplot: Notebook-code
functions: Paragraph
gmres: Paragraph
graph (network): Paragraph
hold on: Paragraph
ilu: Paragraph
indexing arrays: Paragraph
integral: Paragraph
kron: Paragraph
length: Paragraph
minres: Notebook-code
nnz: Paragraph
norm: Notebook-code, Paragraph
ode: Notebook-code
ones: Paragraph
pcg: Paragraph
plot: Paragraph
polyval: Notebook-code
scatter: Paragraph
scientific notation: Paragraph
size: Paragraph
solve: Notebook-code
sparse: Paragraph
spdiags: Paragraph
subplot: Notebook-code
sum: Paragraph
svd: Notebook-code
tic and toc: Paragraph
transpose: Paragraph
vander: Paragraph
zeros: Paragraph
in double precision: Paragraph
Cholesky: Theorem 2.9.3
EVD: Definition 7.2.3
QR: Theorem 3.3.3, Paragraph
SVD: Definition 7.3.1
pivoted LU: Definition 2.6.2
implementation of: Paragraph
- N
- NaN: Paragraph
multidimensional: Algorithm 4.5.1
Frobenius: Paragraph
matrix: Definition 2.7.4, Theorem 7.3.3
- O
- ONC matrix: Definition 3.3.2, Paragraph, ONC matrix
of a finite-difference formula: Definition 5.5.2, Paragraph
of a one-step IVP method: Paragraph
of an approximation: Definition 5.2.2
of numerical integration: Definition 5.6.3
of the finite element method: Paragraph
- P
- PLU factorization: Definition 2.6.2, PLU factorization
:: Paragraph
Images: Paragraph
LinearOperator: Paragraph
NaN: Paragraph
adjoint: Paragraph
animation: Notebook-code, Paragraph
arange: Paragraph
argsort: Paragraph
broadcast: Paragraph
cg: Paragraph
cholesky: Notebook-code
cond: Paragraph, Notebook-code, Paragraph
destructuring: Paragraph
diags: Paragraph
eig: Paragraph
eigs: Paragraph
elementwise multiplication: Paragraph
enumerate: Notebook-code
gmres: Paragraph
hstack: Paragraph
indexing arrays: Paragraph
interp1d: Paragraph
kron: Paragraph
linspace: Paragraph
lstsq: Notebook-code
matrix_power: Notebook-code
max: Paragraph
minres: Notebook-code, Paragraph
networkx: Notebook-code
nnz: Notebook-code
plotting functions: Paragraph
polyfit: Paragraph
quad: Paragraph
return: Paragraph
scientific notation: Paragraph
slice: Paragraph
solve_ivp: Notebook-code
spilu: Paragraph
sum: Paragraph
svd: Paragraph
transpose: Paragraph
triu: Paragraph, Paragraph, Notebook-code
vstack: Paragraph
- Q
- QR factorization: QR factorization
- R
- Rayleigh quotient: Paragraph, Rayleigh quotient
of a linear system: Definition 2.8.2
of rootfinding: Paragraph
multidimensional: Definition 4.5.1
- S
- SPD matrix: SPD matrix See symmetric positive definite matrix
see method of lines: Paragraph
thin form: Paragraph
of IVP solvers: Paragraph
of collocation: Paragraph
of multistep methods: Definition 6.8.1
of polynomial interpolation: Paragraph
- 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
for an IVP: Table 6.6.1, Paragraph, Paragraph
for integration: Definition 5.6.2, Paragraph
of a finite-difference formula: Definition 5.5.1
of a multistep IVP formula: Paragraph
of a numerical integration formula: Definition 5.6.3
of a one-step IVP solver: Paragraph
- U
- unit lower triangular matrix: Paragraph
- V
- Vandermonde matrix: Definition 2.1.2, Paragraph, Vandermonde matrix
- W
- Wedge Antilles: Wedge Antilles, Star Wars: A New Hope
- Y
- Yoda: Yoda, The Empire Strikes Back, Yoda, The Empire Strikes Back, Yoda, The Empire Strikes Back
- Z
- zero-stability: Definition 6.8.1