Madagascar Programming Reference Manual

CONTENTS 5
10 Solvers 201
10.1 Banded matrix solver (banded.c) . . . . . . . . . . . . . . . . . . . . . . . . 201
10.2 Claerbout’s conjugate-gradient iteration (cgstep.c) . . . . . . . . . . . . . . 205
10.3 Conjugate-gradient with shaping regularization (conjgrad.c) . . . . . . . . . 206
10.4 CG with preconditioning (conjprec.c) . . . . . . . . . . . . . . . . . . . . . . 209
10.5 CG iteration (complex data) (cgstep.c) . . . . . . . . . . . . . . . . . . . . . 211
10.6 Conjugate-gradient with shaping regularization for complex numbers (cconjgrad.c)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10.7 Conjugate-direction iteration (cdstep.c) . . . . . . . . . . . . . . . . . . . . 216
10.8 Linked list for use in conjugate-direction-type methods (llist.c) . . . . . . . 219
10.9 Conjugate-direction iteration for complex numbers (ccdstep.c) . . . . . . . . 223
10.10Linked list for CD-type methods (complex data) (clist.c) . . . . . . . . . . . 227
10.11Solving quadratic equations (quadratic.c) . . . . . . . . . . . . . . . . . . . 231
10.12Zero finder (fzero.c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
10.13Runge-Kutta ODE solvers (runge.c) . . . . . . . . . . . . . . . . . . . . . . 233
10.14Solver function for iterative least-squares optimization (tinysolver.c) . . . . 236
10.15Solver functions for iterative least-squares optimization (bigsolver.c) . . . . 237
10.16Weighting for iteratively-reweighted least squares (irls.c) . . . . . . . . . . . 247
10.17Tridiagonal matrix solver (tridiagonal.c) . . . . . . . . . . . . . . . . . . . . 249
11 Interpolation 255
11.1 1-D interpolation (int1.c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
11.2 2-D interpolation (int2.c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.3 3-D interpolation (int3.c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
11.4 Basic interpolation functions (interp.c) . . . . . . . . . . . . . . . . . . . . . 262
11.5 Convert data to B-spline coefficients by fast B-spline transform (prefilter.c) 265
11.6 B-spline interpolation (spline.c) . . . . . . . . . . . . . . . . . . . . . . . . . 267
11.7 Inverse linear interpolation (stretch.c) . . . . . . . . . . . . . . . . . . . . . 271