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J. 17 377-8270Previous HomeINDEXAbramowitz. M., 4Absolute value, 17Acton, F. S.. 104. 146. 162Actuarial calculations, 165Addition of observations in least-squares, 64Algebraic eigenvalue problem. 234ALGOL,13,80,83ALGOL-60,80ALGOL-68, 80Algorithms,informal definition of. 1choice of, 13expression of, 15list of, 255Alternative implementation of singular-valuedecomposition. 38Alternative optima, 230Analytic expression for derivatives, 218.
223Anharmonic oscillator. 138Annihilator of vector. 26APL, 12Argonne National Laboratory, 10Arithmetic.machine, 6operations, 5Autocorrelation, 180Axial search, 171, 178Bisection. 16 1for matrix eigenvalues. 133Björck, A.. 70. 75, 80, 81, 197Bordered matrix. 253Boundary-value problem, 20Bowdler, H. J.. 80Bradbury, W.
W., 244Bremmerman. H.. 147Brent. R. P., 154, 185Brown, K. M.. 146.232Broyden. C. G.. 190Businger. P. A.. 63c (programming language), 11Campey. 182Cancellation of digits. 55Cauchy. A., 186,208Celestial mechanics, 13 1Centroid of points. 168function value at. 172Chambers, J. M., 63Chartres, B. A.. 33, 134Choice.in extended Choleski decomposition, 88of algorithms, 13of algorithms or programs, 14Choleski back-solution, 2 12Choleski decomposition, 13. 27, 84, 136, 2 12, 253extension of. 86Chopping (truncation), 7Cobb-Douglas production function, 144Coefficient matrix, 19, 72Collinearity. 30, 45Column permutations, 75comeig (ALGOL procedure), 110Compactness of programs, 12Comparison of function minimisationalgorithms, 218, 226Compiler for a computer programming language,91Complete matrix eigenvalue problem, 119, 135Complex arithmetic, 83Back-substitution, 72.
75, 86.93. 136with null diagonal elements, 105Back-transformation, 133Backward difference, 2 19Bard, Y.. 207Base period for index numbers. 77BASIC ,11,63,123,127Basis functions, 138Bauer, F., 97Beale, E. M. L., 198Beale-Sorenson formula. 199BFS update of approximate Hessian. 190Bibliography, 263Biggs, M. C., 207271272Compact numerical methods for computersComplex matrix,eigensolutions of, 1 10Complex systems of linear equations, 82Components,principal, 40, 46Computability of a function, 153Computations,statistical, 66Computer,small, 3Conjugacy of search directions, 186, 188, 197,244,245Conjugate gradients, 153, 186, 197, 223, 228, 232,233in linear algebra, 234Constrained optimisation, 3, 218, 221Constraints, 143equality, 221independent, 221inequality, 221Contraction of simplex, 168, 170Convergence,criteria for, 5, 15of inverse iteration, 105of Nelder-Mead search, 180of power method, 103Convergence test, 159, 171, 180, 242for inverse iteration, 108Convex function, 208Corrected R2 statistic, 45Cost of computations, 1, 3Cox, M., 133Cross-products matrix, 49, 66Crout method, 75, 80for complex equations, 83Cubic interpolation, 15 1Cubic inverse interpolation, 159Cubic-parabola problem, 232Cunningham, J., 138,141Cycle or sweep, 35, 49Cyclic Jacobi algorithm, 127Cyclic re-ordering, 98Dahlquist, G., 70, 75, 80, 81, 197Data General computers, see NOVA orECLIPSEData points, 142Davies, 182Davies, Swann and Campey method, 182Decomposition,Choleski, 27of a matrix, 26, 49Definiteness of a matrix, 22Degenerate eigenvalues, 120, 125Degrees of freedom, 46Deletion of observations in least-squares, 64Delta,Kronecker, 3 1, 73, 119Dense matrix, 20, 23Derivative evaluation count, 217Derivatives of a function, 149, 187, 210approximation by differences, 21, 217in minimisation, 143De-scaling,of nonlinear least-squares problem, 223of nonlinear minimisation, 231Descent methods for function minimisation, 186Diagonal matrix, 254Diagonalisation of a real symmetric matrix, 126Difference,replacement of derivative, 21Differential equations,ordinary, 20Digit cancellation, 55Ding Dong matrix, 122, 253Direct method for linear equations, 72Direct search methods for function minimisation182Dixon, L.
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