Numerical Methods Contents - SAM
Numerical Methods Contents - SAM
Numerical Methods Contents - SAM
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scheme<br />
Aitken-Neville, 648<br />
Horner, 632<br />
Schur<br />
Komplement, 95<br />
Schur’s lemma, 399<br />
scientific notation, 107<br />
secant condition, 323<br />
secant method, 288, 323<br />
segmentation<br />
of an image, 427<br />
semi-implicit Euler method, 933<br />
seminorm, 669<br />
sensitivity<br />
of a problem, 136<br />
shape<br />
preservation, 696<br />
preserving spline interpolation, 735<br />
Sherman-Morrison-Woodbury formula, 218<br />
shifted inverse iteration, 440<br />
similarity<br />
of matrices, 398<br />
complete cubic, 728<br />
cubic, 722<br />
cubic, locality, 731<br />
natural cubic, 728<br />
periodic cubic, 729<br />
shape preserving interpolation, 735<br />
stability function<br />
of explicit Runge-Kutta methods, 909<br />
of Runge-Kutta methods, 930<br />
Stable<br />
algorithm, 120<br />
stable<br />
numerically, 120<br />
state space<br />
of an ODE, 830<br />
stationary distribution, 413<br />
steepest descent, 337<br />
stiff IVP, 925<br />
stochastic matrix, 414<br />
stochastic simulation of page rank, 412<br />
Strassen’s algorithm, 42<br />
structurally symmetric matrix, 172<br />
similarity transformations, 398<br />
similary transformation<br />
unitary, 402<br />
Simpson rule, 769<br />
sine<br />
basis, 605<br />
matrix, 605<br />
transform, 606<br />
Sine transform, 605<br />
single precicion, 109<br />
single step method, 848<br />
singular value decomposition, 481, 484<br />
sparse matrix, 139<br />
initialization, 146<br />
LU-factorization, 152<br />
multiplication, 149<br />
sparse matrix storage formats, 141<br />
spectral radius, 397<br />
spectrum, 397<br />
of a matrix, 343<br />
spline<br />
cardinal, 731<br />
sub-matrix, 26<br />
sub-multiplicative, 116<br />
subspace correction, 350<br />
subspace iteration<br />
for direct power method, 455<br />
subspaces<br />
nested, 350<br />
SVD, 481, 484<br />
symmetry<br />
structural, 172<br />
system matrix, 66, 119<br />
system of equations<br />
linear, 66<br />
tagent field, 830<br />
Taylor expansion, 271<br />
Taylor’s formula, 271<br />
tensor product, 31<br />
Teopltiz matrices, 617<br />
termination criterion, 251<br />
Newton iteration, 315<br />
reliable, 252<br />
Ôº ½¿º<br />
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residual based, 253<br />
time-invariant filter, 541<br />
timestep constraint, 910<br />
Toeplitz solvers<br />
fast algorithms, 624<br />
tolerace<br />
absolute, 276<br />
tolerance, 253<br />
absolute, 878<br />
for adaptive timestepping for ODEs, 876<br />
realtive, 878<br />
total least squares, 524<br />
trajectory, 825<br />
transform<br />
cosine, 614<br />
fast Fourier, 594<br />
sine, 606<br />
trapezoidal rule, 769, 862<br />
for ODEs, 862<br />
triangle inequality, 115<br />
tridiagonal matrix, 164<br />
trigonometric basis, 562<br />
List of Symbols<br />
(x k )∗ n (y k ) ˆ= discrete periodic convolution, 548<br />
DΦ ˆ= Jacobian of Φ : D ↦→ R n at x ∈ D, 265<br />
D y f ˆ= Derivative of f w.r.t.. y (Jacobian), 836<br />
J(t 0 ,y 0 ) ˆ= maximal domain of definition of a solution<br />
of an IVP, 837<br />
O ˆ= zero matrix, 27<br />
O(n), 41<br />
E ˆ= expected value of a random variable, 619<br />
R k (m, n), 496<br />
eps ˆ= machine precision, 112<br />
Eig A (λ) ˆ= eigenspace of A for eigenvalue λ,<br />
397<br />
Im(A) ˆ= range/column space of matrix A, 488<br />
Ker(A) ˆ= nullspace of matrix A, 488<br />
trigonometric transformations, 604<br />
trust region method, 538<br />
underflow, 110<br />
unit vector, 24<br />
unitary matrix, 194<br />
unitary similary transformation, 402<br />
upper Hessenberg matrix, 473<br />
upper triangular matrix, 74, 85, 86<br />
Vandermonde matrix, 638<br />
Weddle rule, 770<br />
weight<br />
quadrature, 764<br />
well conditioned, 136<br />
Zerlegung<br />
LU, 93<br />
QR, 227<br />
zero padding, 553<br />
K l (A,z) ˆ= Krylov subspace, 353<br />
‖A‖ 2 F , 496<br />
‖x‖ A ˆ= energy norm induced by s.p.d. matrix<br />
A, 333<br />
‖f‖ L ∞ (I) , 641<br />
‖f‖ L 1 (I) , 642<br />
‖f‖ 2 L 2 (I) , 642<br />
P k , 631<br />
Ψ h y ˆ= discretei evolution for autonomous ODE,<br />
848<br />
S d,M , 721<br />
A + , 505<br />
I ˆ= identity matrix, 27<br />
h ∗ x ˆ= discrete convolution of two vectors, 545<br />
Ôº ½¿º<br />
Ôº ½¿º
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