Compact Numerical Methods for Computers: Linear Algebra and Function MinimisationCRC Press, 1 janv. 1990 - 278 pages This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer. New to the Second Edition The accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software. |
Table des matières
FORMAL PROBLEMS IN LINEAR ALGEBRA | 19 |
HANDLING LARGER PROBLEMS | 49 |
SOME COMMENTS ON THE FORMATION OF THE CROSS | 66 |
THE CHOLESKI DECOMPOSITION | 84 |
THE SYMMETRIC POSITIVE DEFINITE MATRIX AGAIN | 94 |
THE ALGEBRAIC EIGENVALUE PROBLEM | 102 |
REAL SYMMETRIC MATRICES | 125 |
THE GENERALISED SYMMETRIC MATRIX EIGENVALUE | 135 |
DIRECT SEARCH METHODS | 168 |
VARIABLE METRIC | 186 |
CONJUGATE GRADIENTS | 197 |
MINIMISING A NONLINEAR SUM OF SQUARES | 207 |
LEFTOVERS | 218 |
THE CONJUGATE GRADIENTS METHOD APPLIED | 234 |
APPENDICES | 253 |
BIBLIOGRAPHY | 263 |
Autres éditions - Tout afficher
Compact Numerical Methods for Computers: Linear Algebra and Function ... John C. Nash Affichage d'extraits - 1979 |
Compact Numerical Methods for Computers: Linear Algebra and Function ... John C. Nash Affichage d'extraits - 1990 |
Compact Numerical Methods for Computers: Linear Algebra and Function ... John C. Nash Affichage d'extraits - 1979 |
Expressions et termes fréquents
algorithm 22 approximation array axial search b₁ back-substitution begin end begin STEP boolean Bvec Bvec[i calculation Choleski decomposition coefficient columns components computed conjugate gradients algorithm cont convergence test Copyright 1988 J.C.Nash Data General NOVA derivatives diagonal elements digit eigenproblem eigensolutions eigenvalue problem eigenvectors EVALNS evaluations example FORTRAN function minimisation function value Gauss elimination generalised given initial inner product integer inverse iteration ITNS Jacobi algorithm least-squares problems least-squares solution linear equations linear search loop machine precision Marquardt minimum Nash nCol Nelder-Mead nonlinear norm normal equations notcomp Note nRow orthogonal orthogonalisation performed pivoting polytope positive definite procedure Rayleigh quotient real symmetric matrix reduction residual sum root rotation search directions simplex singular values singular-value decomposition solve steepest descent step length stepsize sum of squares symmetric matrix tolerance Turbo Pascal unit matrix variable metric vector Wilkinson writeln zero