Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 1st Edition (Paperback) book cover

Compact Numerical Methods for Computers

Linear Algebra and Function Minimisation, 1st Edition

By John C. Nash

CRC Press

278 pages

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Paperback: 9780852743195
pub: 1990-01-01
$83.95
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Hardback: 9781138413108
pub: 2018-06-28
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pub: 2018-12-13
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Description

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

  • Presents program steps as Turbo Pascal code

  • Includes more algorithmic examples

  • Contains an extended bibliography

    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.

  • Reviews

    Praise for the first edition

    "Anyone who must solve complex problems on a small computer would be well advised to consult Nash's book for both ideas and actual procedures. Those with the luxury of a large-scale computer for their numerical work will also find much of interest here."

    -Peter Castro (Eastman Kodak), Technometrics, 22 February 1980

    Table of Contents

    A starting point

    Formal problems in linear algebra

    The singular-value decomposition and its use to solve least-squares problems

    Handling larger problems

    Some comments on the formation of the cross-product matrix ATA

    Linear equations-a direct approach

    The Choleski decomposition

    The symmetric positive definite matrix again

    The algebraic eigenvalue generalized problem

    Real symmetric matrices

    The generalized symmetric matrix eigenvalue problem

    Optimization and nonlinear equations

    One-dimensional problems

    Direct search methods

    Descent to a minimum I-variable metric algorithms

    Descent to a minimum II-conjugate gradients

    Minimizing a nonlinear sum of squares

    Leftovers

    The conjugate gradients method applied to problems in linear algebra

    Appendices

    Bibliography

    Index

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT000000
    MATHEMATICS / General
    MAT021000
    MATHEMATICS / Number Systems