Page 286 - Compact Numerical Methods For Computers
P. 286
Index 273
Equations, Geradin, M., 244, 246
linear, 19, 20, 51 Gerschgorin bound, 136
Equilibration of matrix, 80 Gerschgorin’s theorem, 121
Equivalent function evaluations (efe’s), 227 Gill, P. E., 221, 225
Euclidean norm, 22 Givens’ reduction, 15, 49, 51, 63, 83
Examples, and singular-value decomposition,
list of, 256 implementation, 54
Execution time, 227 for inverse iteration, 105, 109
Expenditure minimisation, 156 of a real rectangular matrix, 51
Exponents of decimal numbers, 17 operation of, 52
Expression of algorithms, 15 singular-value decomposition and least-squares
Extended precision, 14 solution, 56
Extension of simplex, 168, 169, 172 Givens’ tridiagonalisation, 133
Extrapolation, 151 Global minimum, 146
Golub, G. H., 56
GOTO instructions, 12
False Position, 161
Gradient, 186, 188, 197, 208, 226
Fenton, R. G., 182
computed, 226
Financial Times index, 77 of nonlinear sum of squares, 209
Finkbeiner, D. T., 87
of Rayleigh quotient, 245
Fletcher, R., 190, 192, 198, 199, 215, 228, 244
Gradient calculation in conjugate gradients for
Fletcher-Reeves formula, 199
linear equations, 235
FMIN linear search program, 153
Gradient components,
Ford B., 135
‘large’ computed values of, 206
Formulae,
Gram-Schmidt orthogonalisation, 197
Gauss-Jordan, 98
Gregory, R. T., 117
Forsythe, G. E., 127, 153
FORTRAN, 10, 56, 63 Grid search, 149, 156, 160
Griffith, B. A., 125
Forward difference, 2 19
Guard digits, 7
Forward-substitution, 86, 136
Foster, R. M., 139
Frank matrix, 250,253 Hall, G., 135
Fried, I., 246 Hamiltonian operator, 28, 138
Fröberg, C., 21, 127, 238, 251 Hammarling, S., 50
Full-rank case, 23, 66 Hanson, R. J., 64
Function evaluation count, 157, 164, 209, 217, Hartley, H. O., 210, 211
227, 232 Harwell subroutine library, 215
Function minimisation, 142, 207 Hassan, Z., 223
Functions, Healy, M. J. R., 88, 90
penalty, 222 Heaviside function, 222
Hemstitching of function minimisation method,
186, 208
Galle, 131
Gauss elimination, 72, 79, 82, 93 Henderson, B., 153
for inverse iteration, 105, 109 Henrici, P., 127, 162
variations, 80 Hermitian matrix, 137
with partial pivoting, 75 Hessian, 189, 197, 231
Gauss-Jordan reduction, 82, 93 for Rayleigh quotient, 244
Gauss-Newton method, 209, 211, 228 matrix, 187
Gearhart, W. B., 146, 232 Hestenes, M. R., 33, 134, 235, 241
Generalised eigenvalue problem, 135, 234, 242 Heuristic method, 168, 171
Generalised inverse, 44, 66 Hewlett-Packard,
2 and 4 condition, 26 computers, see HP9830
of a matrix, 24 pocket calculators, 5
Generalised matrix eigenvalue problem, 28, 104 Hilbert segment, 108, 253
Gentleman, W. M., 50 Hillstrom, K. E., 227
