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Index of MATLAB Programs




forward row Forward substitution: row-oriented version . 66
forward col Forward substitution: column-oriented version 66
backward col Backward substitution: column-oriented version 66
lu kji LU factorization of matrix A. kji version . . 77
lu jki LU factorization of matrix A. jki version . . 77
lu ijk LU factorization of the matrix A: ijk version 79
chol2 Cholesky factorization . . . . . . . . . . . . . 81
mod grams Modi¬ed Gram-Schmidt method . . . . . . . 84
LUpivtot LU factorization with complete pivoting . . . 88
lu band LU factorization for a banded matrix . . . . 92
forw band Forward substitution for a banded matrix L 92
back band Backward substitution for a banded matrix U 92
mod thomas Thomas algorithm, modi¬ed version . . . . . 93
cond est Algorithm for the approximation of K1 (A) . 109
JOR JOR method . . . . . . . . . . . . . . . . . . 135
SOR SOR method . . . . . . . . . . . . . . . . . . 136
basicILU Incomplete LU factorization . . . . . . . . . 141
ilup ILU(p) factorization . . . . . . . . . . . . . . 143
gradient Gradient method with dynamic parameter . 149
conjgrad Preconditioned conjugate gradient method . 157
arnoldi alg The Arnoldi algorithm . . . . . . . . . . . . 161
arnoldi met The Arnoldi method for linear systems . . . 164
GMRES The GMRES method for linear systems . . . 166
Lanczos The Lanczos method for linear systems . . . 167
Lanczosnosym The Lanczos method for unsymmetric systems 170
644 Index of MATLAB Programs

powerm Power method . . . . . . . . . . . . . . . . . 197
invpower Inverse power method . . . . . . . . . . . . . 198
basicqr Basic QR iteration . . . . . . . . . . . . . . . 203
houshess Hessenberg-Householder method . . . . . . . 208
hessqr Hessenberg-QR method . . . . . . . . . . . . 210
givensqr QR factorization with Givens rotations . . . 211
vhouse Construction of the Householder vector . . . 213
givcos Computation of Givens cosine and sine . . . 214
Product G(i, k, θ)T M . . . . . . . . . . . . .
garow 214
gacol Product MG(i, k, θ) . . . . . . . . . . . . . . 214
qrshift QR iteration with single shift . . . . . . . . . 217
qr2shift QR iteration with double shift . . . . . . . . 220
psinorm Evaluation of Ψ(A) . . . . . . . . . . . . . . 229
symschur Evaluation of c and s . . . . . . . . . . . . . 229
cycjacobi Cyclic Jacobi method for symmetric matrices 229
sturm Sturm sequence evaluation . . . . . . . . . . 232
givsturm Givens method using the Sturm sequence . . 232
chcksign Sign changes in the Sturm sequence . . . . . 232
Calculation of the interval J = [±, β] . . . .
bound 232
eiglancz Extremal eigenvalues of a symmetric matrix 234
bisect Bisection method . . . . . . . . . . . . . . . 250
chord The chord method . . . . . . . . . . . . . . . 254
secant The secant method . . . . . . . . . . . . . . 255
regfalsi The Regula Falsi method . . . . . . . . . . . 255
newton Newton™s method . . . . . . . . . . . . . . . 255
¬xpoint Fixed-point method . . . . . . . . . . . . . . 260
horner Synthetic division algorithm . . . . . . . . . 263
newthorn Newton-Horner method with re¬nement . . . 266
mullde¬‚ Muller™s method with re¬nement . . . . . . . 269
aitken Aitken™s extrapolation . . . . . . . . . . . . . 274
adptnewt Adaptive Newton™s method . . . . . . . . . . 276
newtonxsys Newton™s method for nonlinear systems . . . 285
broyden Broyden™s method for nonlinear systems . . . 290
¬xposys Fixed-point method for nonlinear systems . . 293
hookejeeves The method of Hooke and Jeeves (HJ) . . . 296
explore Exploration step in the HJ method . . . . . 297
backtrackr Backtraking for line search . . . . . . . . . . 303
lagrpen Penalty method . . . . . . . . . . . . . . . . 316
lagrmult Method of Lagrange multipliers . . . . . . . 319
interpol Lagrange polynomial using Newton™s formula 334
dividif Newton divided di¬erences . . . . . . . . . . 336
hermpol Osculating polynomial . . . . . . . . . . . . . 342
par spline Parametric splines . . . . . . . . . . . . . . . 359
bernstein Bernstein polynomials . . . . . . . . . . . . . 361
bezier B´zier curves . . . . . . . . . . . . . . . . . .
e 361
Index of MATLAB Programs 645

midpntc Midpoint composite formula . . . . . . . . . 375
trapezc Composite trapezoidal formula . . . . . . . . 376
simpsonc Composite Cavalieri-Simpson formula . . . . 377
newtcot Closed Newton-Cotes formulae . . . . . . . . 383
trapmodc Composite corrected trapezoidal formula . . 387
romberg Romberg integration . . . . . . . . . . . . . . 391
simpadpt Adaptive Cavalieri-Simpson formula . . . . . 397
redmidpt Midpoint reduction formula . . . . . . . . . . 404
redtrap Trapezoidal reduction formula . . . . . . . . 404
midptr2d Midpoint rule on a triangle . . . . . . . . . . 406
traptr2d Trapezoidal rule on a triangle . . . . . . . . 406
coe¬‚ege Coe¬cients of Legendre polynomials . . . . . 430
coe¬‚agu Coe¬cients of Laguerre polynomials . . . . . 430
coefherm Coe¬cients of Hermite polynomials . . . . . 430
zplege Coe¬cients of Gauss-Legendre formulae . . . 430
zplagu Coe¬cients of Gauss-Laguerre formulae . . . 430
zpherm Coe¬cients of Gauss-Hermite formulae . . . 430
dft Discrete Fourier transform . . . . . . . . . . 439
idft Inverse discrete Fourier transform . . . . . . 439
¬trec FFT algorithm in the recursive version . . . 441

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