Numerical Methods Contents - SAM

linear in Gauss-Newton method, 538
local, 241
local quadratic in damped Newton method, 537
quadratic, 249
rate, 243
convergence monitor
of Broyden method, 327
convolution
discrete, 541, 545
discrete periodic, 548
of sequences, 545
cosine
basis, 614
transform, 614
cosine matrix, 614
cosine transform, 614
costs
Cholesky decomposition, 187
Crout’s algorithm, 90
CRS, 141
CRS format
diagonal, 143
divided differences, 658
dot product, 31
double precision, 109
economical singular value decomposition, 487
efficiency, 296
eigenspace, 397
eigenvalue, 397
eigenvector, 397
electric circuit, 67, 235
resonant frequencies, 392
elementary arithmetic operations, 106, 112
energy norm, 333
envelope
matrix, 166
Equation
non-linear, 238
ergodicity, 420
error behavior
asymptotic, 662
error estimator
a posteriori, 255
cubic Hermite interpolation, 641
damped Newton method, 318
damping factor, 319
deblurring, 585
definite, 115
dense matrix, 139
DFT, 555, 565
two-dimensional, 584
Diagonal dominance, 182
diagonal matrix, 86
diagonalization
of a matrix, 400
diagonalization of local translation invariant linear
operators, 609
difference quotient, 308
difference scheme, 842
differential in non-linear least squares, 306
direct power method, 422
discrete convolution, 541, 545
discrete Fourier transform, 555, 565
discrete periodic convolution, 548
Euler method
explicit, 841
implicit, 844
semi implicit, 933
Euler polygon, 842
Euler’s iteration, 287
expansion
asymptotic, 652
explicit Euler method, 841
Butcher scheme, 866
explicit midpoint rule
Butcher scheme, 866
for ODEs, 862
explicit Runge-Kutta method, 864
explicit trapzoidal rule
Butcher scheme, 866
exponential convergence, 680
extended state space
of an ODE, 830
extrapolation, 652
fast Fourier transform, 594
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FFT, 594
fill-in, 153
filter
high pass, 574
low pass, 574
finite filter, 541
fit
polynomial, 502
fixed point, 259
fixed point form, 259
fixed point iteration
consistency, 259
floating point numbers, 107
forward substitution, 93
Fourier
matrix, 563
Fourier transform
discrete, 555, 565
fractional order of convergence, 290
frequency filtering, 568
Funktion
shandles, 302
Halley’s iteration, 280, 287
harmonic mean, 716
heartbeat model, 826
Hermite interpolation
cubic, 641
Hessian matrix, 306
high pass filter, 574
homogeneous, 115
Horner scheme, 632
Householder reflection, 197
IEEE standard 754, 109
ill conditioned, 136
image segmentation, 427
implicit Euler method, 844
impulse response
of a filter, 541
in place, 78, 90, 92
in situ, 92
in-situ, 78
increment equations
linearized, 934
fzero, 277
Gauss Quadrature, 792
Gauss-Newton method, 533
Gauss-Seidel preconditioner, 376
Gaussian elimination, 72
block version, 80
for non-square matrices, 81
instability, 134
Gerschgorin circle theorem, 398
Givens rotation, 200, 220
Givens-Rotation, 211, 230, 233
global solution
of an IVP, 837
GMRES, 386
restarted, 386
Golub-Welsch algorithm, 805
gradient, 306, 338
Gram-Schmidt
Orthonormalisierung, 471
Gram-Schmidt orthogonalization, 356, 471
grid function, 610
increments
Runge-Kutta, 864, 928
inductance, 68
inductor, 68
inf, 110
infinity, 110
initial guess, 240, 258
initial value problem
stiff, 925
initial value problem (IVP), 829
inner product
A-, 333
intermediate value theorem, 275
interpolation
barycentric formula, 647
Chebychev, 670
complete cubic spline, 728
general polynomial, 634
Hermite, 634
Lagrange, 633
natural cubic spline, 728
periodic cubic spline, 729
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