Page 285 - Compact Numerical Methods For Computers
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272 Compact numerical methods for computers
Complex matrix, Deletion of observations in least-squares, 64
eigensolutions of, 1 10 Delta,
Complex systems of linear equations, 82 Kronecker, 3 1, 73, 119
Components, Dense matrix, 20, 23
principal, 40, 46 Derivative evaluation count, 217
Computability of a function, 153 Derivatives of a function, 149, 187, 210
Computations, approximation by differences, 21, 217
statistical, 66 in minimisation, 143
Computer, De-scaling,
small, 3 of nonlinear least-squares problem, 223
Conjugacy of search directions, 186, 188, 197, of nonlinear minimisation, 231
244,245 Descent methods for function minimisation, 186
Conjugate gradients, 153, 186, 197, 223, 228, 232, Diagonal matrix, 254
233 Diagonalisation of a real symmetric matrix, 126
in linear algebra, 234 Difference,
Constrained optimisation, 3, 218, 221 replacement of derivative, 21
Constraints, 143 Differential equations,
equality, 221 ordinary, 20
independent, 221 Digit cancellation, 55
inequality, 221 Ding Dong matrix, 122, 253
Contraction of simplex, 168, 170 Direct method for linear equations, 72
Convergence, Direct search methods for function minimisation
criteria for, 5, 15 182
of inverse iteration, 105 Dixon, L. C., 154, 182, 223, 225
of Nelder-Mead search, 180 Doolittle method, 75, 80
of power method, 103 Double precision, 9, 14, 81, 83, 91
Convergence test, 159, 171, 180, 242 Dow Jones index, 77
for inverse iteration, 108
Convex function, 208 E (notation), 17
Corrected R 2 statistic, 45 Eason, E. D., 182
Cost of computations, 1, 3 Eberlein, P., 110, 117
Cox, M., 133 ECLIPSE, 52, 96, 128, 153, 156, 159
Cross-products matrix, 49, 66 Effect of Jacobi rotations, 126
Crout method, 75, 80 Eigenproblem,
for complex equations, 83 generalised, 104
Cubic interpolation, 15 1 total or complete, 119
Cubic inverse interpolation, 159 Eigenproblem of a real symmetric matrix,
Cubic-parabola problem, 232 comparison of methods, 133
Cunningham, J., 138,141 Eigensolutions, 28, 31
Cycle or sweep, 35, 49 by singular-value decomposition, 123
Cyclic Jacobi algorithm, 127 of a complex matrix, 117
Cyclic re-ordering, 98 of a real symmetric matrix, 119
Eigenvalue, 28, 135
Dahlquist, G., 70, 75, 80, 81, 197 degenerate, 103
Data General computers, see NOVA or Eigenvalue approximation in inverse iteration,
ECLIPSE 108
Data points, 142 Eigenvalue decomposition of matrix, 135
Davies, 182 Eigenvalue problem,
Davies, Swann and Campey method, 182 matrix or algebraic, 102
Decomposition, Eigenvector, 28, 135
Choleski, 27 Elementary matrices, 73
of a matrix, 26, 49 Elementary operations on matrices, 73
Definiteness of a matrix, 22 Elimination method for linear equations, 72
Degenerate eigenvalues, 120, 125 Elimination of constraints, 22 1
Degrees of freedom, 46 choice in, 223
