1st Edition

Compact Numerical Methods for Computers Linear Algebra and Function Minimisation

By John C. Nash Copyright 1990
    290 Pages
    by CRC Press

    290 Pages
    by CRC Press

    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.
  • 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
    The conjugate gradients method applied to problems in linear algebra


    John C. Nash

    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