Page 289 - Compact Numerical Methods For Computers

276 Compact numerical methods for computers
Normalising constant, 139 Plauger, P. J., 12
Notation, 17 Plot or graph of function, 151
NOVA, 5, 46, 69, 79, 90, 91, 93, 100, 108, 109, Polak, E., 198, 199
117, 122, 123, 125, 127, 141, 153, 156, 164, Polak-Ribiere formula, 199
199, 206, 208, 220, 225,226, 229, 230,232, Polynomial roots, 143, 145
241,250 Positive definite iteration matrix, 192
Null vector, 20 Positive definite matrix, 22, 120, 188, 197, 211,
Numerical Algorithms Group, 10 235, 241, 243
Numerical approximation of derivatives, 2 17, Positive definite symmetric matrix, 83
218, 223, 228 inverse of, 24
Numerical differentiation, 218 Powell. M. J. D., 185, 199
Power method for dominant matrix
Objective function, 205, 207 eigensolution, 102
Oliver, F. R., 144, 207 Precision,
One-dimensional problems, 148 double, 9, 14
O’Neill, R., 171, 178 extended, 9, 14
One-sided transformation, 136 machine, 5, 46, 70
Ones matrix, 254 Price, K., 90
Operations, Principal axes of a cube, 125
arithmetic, 5 Principal components, 41, 46
Optimisation, 142 Principal moments of inertia, 125
constrained, 3 Product of triangular matrices, 74
Ordering of eigenvalues, 127, 134 Program,
Ordinary differential equations, 20 choice, 14
Orthogonal vectors, 25, 32 coding, 14
Orthogonalisation, compactness, 12
by plane rotations, 32 maintenance, 14
of matrix rows, 49, 54 readability, 12
Orthogonality, reliability, 14
of eigenvectors of real symmetric matrix, 119 testing, 14
of search directions, 198 Programming,
of vectors, 26 mathematical, 13
Osborne, M. R., 85, 142, 186, 226 structured, 12
Programming language, 11, 15
Programs,
Paige, C. C., 234 manufacturers’, 9
Parabolic interpolation, 151 sources of, 9
Parabolic inverse interpolation, 152, 199, 210 Pseudo-random numbers, 147, 166, 240
formulae, 153
Parameters, 142
Parlett, B. N., 234 QR algorithm, 133
Partial penalty function, 222 QR decomposition, 26, 49, 50, 64
Partial pivoting, 75 Quadratic equation, 85, 244
Pascal, 12 Quadratic form, 22, 89, 190, 198, 235
Pauling, L., 28 Quadratic or parabolic approximation, 15 1
Penalty functions, 222, 223 Quadratic termination, 188, 199, 236
Penrose, R., 26 Quantum mechanics, 28
Penrose conditions for generalised inverse, 26 Quasi-Newton methods, 187
Permutations or interchanges, 75
Perry, A., 144, 230
2
Peters, G., 105 R statistic, 45, 63
Pierce, B. O., 139 Radix, 7
Pivoting, 75, 93, 95, 97 Ralston, A., 95, 104, 121, 127, 218
Plane rotation, 32, 49, 54, 126 Rank, 20
formulae, 34 Rank-deficient case, 24, 25, 55