Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation

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CRC Press, 1 de gen. 1990 - 278 pàgines
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.
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    Continguts

    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

    OPTIMISATION AND NONLINEAR EQUATIONS
    142
    ONEDIMENSIONAL PROBLEMS
    148

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