Page 268 - Compact Numerical Methods For Computers

Appendix 2

LIST OF ALGORITHMS

Algorithm 1. Singular-value decomposition 36
Algorithm 2. Least-squares solution via singular-value decomposition 42
Algorithm 3. Givens’ reduction of a real rectangular matrix 51
Algorithm 4. Givens’ reductions, singular-value decomposition and least-
squares solution 56
Algorithm 5. Gauss elimination with partial pivoting 75
Algorithm 6. Gauss elimination back-substitution 77
Algorithm 7. Choleski decomposition in compact storage 88
Algorithm 8. Choleski back-substitution 89
Algorithm 9. Bauer-Reinsch inversion of a positive definite symmetric
matrix 99
Algorithm 10. Inverse iteration via Gauss elimination 106
Algorithm 11. Standardisation of a complex vector 111
Algorithm 12. Residuals of a complex eigensolution 112
Algorithm 26. Eigensolutions of a complex matrix by Eberlein’s method 113
Algorithm 13. Eigensolutions of a real symmetric matrix via the singular-
value decomposition 123
Algorithm 14. A Jacobi algorithm for eigensolutions of a real symmetric
matrix 128
Algorithm 15. Solution of a generalised matrix eigenvalue problem by two
applications of the Jacobi algorithm 137
Algorithm 16. Grid search along a line 149
Algorithm 17. Minimisation of a function of one variable 154
Algorithm 18. Root-finding by bisection and False Position 162
Algorithm 19. A Nelder-Mead minimisation procedure 173
Algorithm 20. Axial search 179
Algorithm 27. Hooke and Jeeves minimiser 183
Algorithm 21. Variable metric minimiser 192
Algorithm 22. Function minimisation by conjugate gradients 200
Algorithm 23. Modified Marquardt method for minimising a nonlinear
sum-of-squares function 212
Algorithm 24. Solution of a consistent set of linear equations by conjugate
gradients 236
Algorithm 25. Rayleigh quotient minimisation by conjugate gradients 246

255