Page 291 - Compact Numerical Methods For Computers

278 Compact numerical methods for computers

Step length for derivative approximation, 219 Truncation, 7
Stepwise regression, 96 Two-point boundary value problem, 238
Stewart, G. W., 40, 234
Structured programming, 12
Styan, G. P. H., 56 Unconstrained minimisation. 142
Substitution for constraints, 221 Uncorrelated residuals, 56, 70
Success-failure, Uniform distribution. 167
algorithm, 151, 153 Unimodal function, 149
search, 152 Unit matrix, 29
Success in function minimisation, 226 Univac 1108, 56, 120
Sum of squares, 22, 23, 39,42, 55, 79 Updating,
and cross products, 66 formula, 190
nonlinear, 207 of approximate Hessian, 189, 192
total, 45
Surveying-data fitting, 24, 240 V-shaped triple of points, 152
Swann, 182, 225 Values,
Sweep or cycle. 35, 49, 126 singular, see Singular values
Symmetric matrix, 135, 243 Varga, R. S., 83
Symmetry. Variable metric.
use in eigensolution program, 134 algorithms, 198
Synge, J. L., 125 methods, 186, 187, 223, 228, 233
System errors, 4 Variables. 142
Variance computation in floating-point
Taylor serves, 190, 209 arithmetic. 67
Tektronix 4051, 156 Variance of results from ‘known’ values, 241
Test matrices, 253 Variation method, 28
Test problems, 226 Vector. 19, 30
Time series, 180 null, 20. 32
Tolerance, 5, 15, 35, 40, 54 residual. 21
for acceptable point search, 190
for conjugate gradients least-squares, 240 Weighting.
for deviation of parameters from target, 204 for nonlinear least-squares, 207
for inverse iteration by conjugate gradients, of constraints, 222
243 in index numbers. 77
Total sum of squares, 45 Wiberg, T., 242
Transactions on Mathematical Software. 11 Wilkinson, J. H., 13, 28, 75, 83. 86, 97, 102, 105,
Transposition, 22 110, 119, 127, 133, 137, 251, 253, 254
Traub, J. F., 143, 148 W+matrix, 254
Trial function, 28 W- matrix, 108, 254
Triangle inequality, 22 Wilson, E. B., 28
Triangular decomposition, 74
Triangular matrix, 72
Yourdon. E., 12
Triangular system,
of equations, 72
of linear equations, 51 Zambardino, R. A., 13
Tridiagonal matrix, 251