Page 290 - Compact Numerical Methods For Computers

Index 277

Rayleigh quotient, 122, 123, 138, 200, 234, 242, Saunders, M. A., 234
244 Scaling,
minimisation, 250 of Gauss -Newton method, 211
minimisation by conjugate gradients, 243 of linear equations, 80
Rayleigh-Ritz method, 138 Schwarz, H. R., 127
Readability of programs, 12 Search,
Real symmetric matrix, 119 along a line, 143, 148
Reconciliation of published statistics, 204 directions, 192, 197
Recurrence relation, 166, 198, 235, 246 Sebastian, D. J., 190
Reduction, Secant algorithm, 162
of simplex, 168, 170 Seidel, L., 131
to tridiagonal form, 133 sgn (Signum function), 34
Reeves, C. M., 198, 199 Shanno, D. F., 190
References, 263 Shift of matrix eigenvalues, 103, 121, 136, 242
Reflection of simplex, 168, 169, 172 Shooting method, 239
Regression, 92 Short word-length arithmetic, 159, 191
stepwise, 96 Signum function, 34
Reid, J. K., 234 Simplex, 168
Reinsch, C., 13, 83, 97, 102, 110, 133, 137, 251 size, 171
Reliability, 14 Simulation of insurance scheme, 165
Re-numeration, 98 Simultaneous equations,
Re-ordering, 99 linear, 19
Residual, 21, 45, 250 nonlinear, 142, 144
uncorrelated, 56, 70 Single precision, 134, 159
weighted, 24 Singular least-squares problem, 240
Residuals, 142, 144, 207 Singular matrix, 20
for complex eigensolutions, 117 Singular-value decomposition, 26, 30, 31, 54, 66,
for eigensolutions, 125, 128 69, 81, 119
sign of, 142, 207 algorithm, 36
Residual sum of squares, 55, 79 alternative implementation, 38
computation of, 43 updating of, 63
Residual vector, 242 Singular values, 30, 31, 33, 54, 55
Restart, ordering of, 33
of conjugate gradients for linear equations, 236 ratio of, 42
of conjugate gradients minimisation, 199 Small computer, 3
of Nelder-Mead search, 171 Software,
Ribiere, G., 198, 199 mathematical, 10
Ris, F. N., 253 Soland, R. M., 144, 230
Root-finding, 143, 145, 148, 159, 160,239 Solution,
Roots, least-squares, 22
of equations, 142 minimum-length least-squares, 22
of quadratic equation, 245 Sorenson, H. W., 198
Rosenbrock, H. H., 151, 182, 196, 208, 209 Sparse matrix, 20, 23, 102, 234
Rounding, 7 Spendley, W., 168
Row, ‘Square-root-free Givens’ reduction, 50
orthogonalisation, 49, 54 Standardisation of complex eigenvector, 111
permutations, 75 Starting points, 146
Ruhe, A., 234, 242 Starting vector,
Rutishauser, H., 127, 134 power method, 104
Statistical computations, 66
Steepest descent, 186, 199, 208, 209, 211
Saddle points, 143, 146, 159, 208 Stegun, I. A., 4
Safety check (iteration limit), 128 Step adjustment in success-failure algorithm, 154
Sampson, J. H., 74 Step length, 178, 187, 197, 200, 242
Sargent, R. W. H., 190 Step-length choice, 158