Numerical Methods Contents - SAM

x∗ n y ˆ= discrete periodic convolution of vectors,
548
M ˆ= set of machine numbers, 106
δ ij ˆ= Kronecker symbol, 24
κ(A) ˆ= spectral condition number, 348
λ max ˆ= largest eigenvalue (in modulus), 348
λ min ˆ= smalles eigenvalue (in modulus), 348
1 = (1,...,1) T , 909, 930
Ncut(X) ˆ= normalized cut of subset of weighted
graph, 430
cond(A), 132
cut(X) ˆ= cut of subset of weighted graph, 430
env(A), 166
nnz, 139
rank(A) ˆ= rank of matrix A, 70
rd, 111
weight(X) ˆ= connectivity of subset of weighted
graph, 430
m(A), 164
ρ(A) ˆ= spectral radius of A ∈ K n,n , 397
ρ A (u) ˆ= Rayleigh quotient, 423
f ˆ= right hand side of an ODE, 830
σ(M) hat= spectrum of matrix M, 343
˜⋆, 111
m(A), 164
m(A), 164
y[t i , ...,t i+k ] ˆ= divided difference, 658
‖ x ‖ 1 , 115
‖ x ‖ 2 , 115
‖ x ‖ ∞ , 115
˙ ˆ= Derivative w.r.t. time t, 823
TOL tolerance, 876
Ôº ½¿º
Evolution operator, 839
Explicit Runge-Kutta method, 864
Fill-In, 153
Frobenius norm, 496
function
concave, 691
convex, 691
Hessian matrix, 306
Inverse of a matrix, 70
Krylov space, 353
L-stable Runge-Kutta method, 931
Lebesgue constant, 643
Legendre polynomials, 799
Linear convergence, 243
Lipschitz continuos function, 835, 836
machine numbers, 108
matrix
generalized condition number, 506
s.p.d, 179
Single step method, 848
symmetric positive definite, 179
Matrix envelope, 166
matrix norm, 116
monotonic data, 689
norm, 115
Frobenius norm, 496
Normalized cut, 430
numerical algorithm, 119
Order of convergence, 247
orthogonal matrix, 194
Permutation matrix, 102
polynomial
Bernstein, 754
Chebychev, 671
generalized Lagrange, 640
pseudoinverse, 505
Rank of a matrix, 70
Rayleigh quotient, 423
residual, 126
Runge-Kutta method, 928
Ôº½ ½¿º
singular value decomposition (SVD), 484
sparse matrices, 139
List of Definitions
sparse matrix, 139
splines, 721
stable algorithm, 120
Arrow matrix, 156
Bézier curves, 757
Bernstein polynomials, 754
Chebychev polynomial, 671
circulant matrix, 551
concave
data, 690
function, 691
Condition (number) of a matrix, 132
Consistency of fixed point iterations, 259
Consistency of iterative methods, 240
Contractive mapping, 263
Convergence, 240
local, 241
convex
data
data, 690
function, 691
concave, 690
convex, 690
Diagonally dominant matrix, 182
Discrete convolution, 545
discrete Fourier transform, 565
discrete periodic convolution, 548
eigenvalues and eigenvectors, 397
energy norm, 333
Ôº¼ ½¿º
Structurally symmetric matrix, 172
Toeplitz matrix, 620
Types of matrices, 86
unitary matrix, 194
Ôº¾ ½¿º
global, 241
equivalence of norms, 243