Page 287 - Compact Numerical Methods For Computers

274 Compact numerical methods for computers

Homogeneity of a function, 244 Jacobi, C.G. J., 126. 127, 131
Hooke and Jeeves method, 182 jacobi (ALGOL procedure), 128, 133
Householder tridiagonalisation, 133 Jacobi algorithm, 126, 136,250
HP9830, 44, 56, 62, 70, 90, 92, 131, 164 cyclic, 127
organisation of, 128
Jacobi rotations,
effect of, 126
IBM 370, 120 Jacobian, 211, 217, 232
IBM 370/168, 56, 128, 167, 196, 239 matrix, 209
I11 conditioning of least-squares problem, 42
Jaffrelot, J. J., 204
Implicit interchanges for pivoting, 81
Jeeves, 185
IMSL, 10
Jenkins, M. A., 143, 148
Indefinite systems of linear equations. 241
Jones, A., 215
Independence,
linear, 20
Kahan, W., 234
Index array, 82
Index numbers, 23, 77 Kaiser, H. F., 134
Infeasible problems, 221 Karney, D. L., 117
Infinity norm, 104 Kendall, M. G., 40, 180
Information loss, 67 Kernighan, B. W., 12
Kowalik, J., 85, 142, 186
Initial values for parameters, 146
Kronecker delta, 3 173, 119
Inner product, 28, 245
Insurance premium calculation. 165
T
Interchange, LL decomposition, 84
implicit, 81 Lagrange multipliers, 221
row and column, 95 Lanczos method for eigenvalue problems. 234
Internal rate of return, 145 Lawson, C. L., 64
International Mathematical and Statistical Least-squares, 23, 50, 54, 77
Libraries, 10 linear, 21
Interpolating parabola, 152 via normal equations, 92
Interpolation, via singular-value decomposition, 40, 42
formulae for differentiation, 218 Least-squares computations,
linear, 161 example, 45
Interpreter for computer programming language, Least-squares solution, 22
91 Lefkovitch, L. P., 56, 63, 70
Interval, Levenberg, K., 211
closed, 17 Leverrier, 131
for linear search, 148 Linear algebra, 19
for root-finding, 160 Linear approximation of nonlinear function. 187
open, 17 Linear combination, 29
Inverse, Linear dependence, 34
generalised, 44 Linear equations, 19, 20, 72, 77, 93, 234, 235
of a matrix, 24 as a least-squares problem, 23
of a symmetric positive definite matrix, 97 complex, 82
of triangular matrices, 74 consistent, 87
Inverse interpolation, 151 Linear independence, 20, 25
Inverse iteration, 104, 140 Linear least-squares, 21, 77, 207, 234, 235
behaviour of, 108 Linear relationship, 23
by conjugate gradients, 241,249 Linear search, 143, 146, 148, 156, 159, 188, 189,
Inverse linear interpolation, 161 192, 198, 199, 235, 244
Inverse matrix, 95 acceptable point strategy, 190
Iteration limit, 109 List of algorithms. 255
Iteration matrix, 188 List of examples, 256
initialisation, 191 Local maxima, 143. 146, 149
Iterative improvement of linear-equation Local minima, 146, 208
solutions, 81 Logistic growth function, 144, 216