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Handbook for Automatic Computation

Volume II: Linear Algebra

  • Book
  • © 1971

Overview

Authors:
  1. J. H. Wilkinson

    1. Division of Numerical & Applied Mathematics, National Physical Laboratory, Teddington, Middlesex, Great Britain

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  2. C. Reinsch

    1. Mathematisches Institut, Technischen Universität, 8 München 2, Deutschland

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Editors:
  1. F. L. Bauer

    1. Mathematisches Institut, Technichen Universität, 8 München 2, Deutschland

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  2. A. S. Householder
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  3. F. W. J. Olver
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  4. H. Rutishauser

    1. Fachgruppe Computer-Wissenschaften, Eidgenössische Technische Hochschule Zürich, Zürich, Schweiz

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  5. K. Samelson
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  6. E. Stiefel
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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 186)

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Table of contents (29 chapters)

  1. Front Matter

    Pages I-IX
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  2. Linear Systems, Least Squares and Linear Programming

    1. Front Matter

      Pages 1-8
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    2. Symmetric Decomposition of a Positive Definite Matrix

      • R. S. Martin, G. Peters, J. H. Wilkinson
      Pages 9-30

    3. Iterative Refinement of the Solution of a Positive Definite System of Equations

      • R. S. Martin, G. Peters, J. H. Wilkinson
      Pages 31-44

    4. Inversion of Positive Definite Matrices by the Gauss-Jordan Method

      • F. L. Bauer, C. Reinsch
      Pages 45-49

    5. Symmetric Decomposition of Positive Definite Band Matrices

      • R. S. Martin, J. H. Wilkinson
      Pages 50-56

    6. The Conjugate Gradient Method

      • T. Ginsburg
      Pages 57-69

    7. Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices

      • R. S. Martin, J. H. Wilkinson
      Pages 70-92

    8. Solution of Real and Complex Systems of Linear Equations

      • H. J. Bowdler, R. S. Martin, G. Peters, J. H. Wilkinson
      Pages 93-110

    9. Linear Least Squares Solutions by Housholder Transformations

      • P. Businger, G. H. Golub
      Pages 111-118

    10. Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems

      • F. L. Bauer
      Pages 119-133

    11. Singular Value Decomposition and Least Squares Solutions

      • G. H. Golub, C. Reinsch
      Pages 134-151

    12. A Realization of the Simplex Method Based on Triangular Decompositions

      • R. H. Bartels, J. Stoer, Ch. Zenger
      Pages 152-190

  3. The Algebraic Eigenvalue Problem

    1. Front Matter

      Pages 191-201
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    2. The Jacobi Method for Real Symmetric Matrices

      • H. Rutishauser
      Pages 202-211

    3. Householder’s Tridiagonalization of a Symmetric Matrix

      • R. S. Martin, C. Reinsch, J. H. Wilkinson
      Pages 212-226

    4. The QR and QL Algorithms for Symmetric Matrices

      • H. Bowdler, R. S. Martin, C. Reinsch, J. H. Wilkinson
      Pages 227-240

    5. The Implicit QL Algorithm

      • A. Dubrulle, R. S. Martin, J. H. Wilkinson
      Pages 241-248

    6. Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection

      • W. Barth, R. S. Martin, J. H. Wilkinson
      Pages 249-256

    7. Rational QR Transformation with Newton Shift for Symmetric Tridiagonal Matrices

      • C. Reinsch, F. L. Bauer
      Pages 257-265
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Keywords

About this book

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.

Authors, Editors and Affiliations

  • Mathematisches Institut, Technichen Universität, 8 München 2, Deutschland

    F. L. Bauer

  • Fachgruppe Computer-Wissenschaften, Eidgenössische Technische Hochschule Zürich, Zürich, Schweiz

    H. Rutishauser

  • Division of Numerical & Applied Mathematics, National Physical Laboratory, Teddington, Middlesex, Great Britain

    J. H. Wilkinson

  • Mathematisches Institut, Technischen Universität, 8 München 2, Deutschland

    C. Reinsch

Bibliographic Information

  • Book Title: Handbook for Automatic Computation

  • Book Subtitle: Volume II: Linear Algebra

  • Authors: J. H. Wilkinson, C. Reinsch

  • Editors: F. L. Bauer, A. S. Householder, F. W. J. Olver, H. Rutishauser, K. Samelson, E. Stiefel

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-86940-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1971

  • Softcover ISBN: 978-3-642-86942-6Published: 23 August 2014

  • eBook ISBN: 978-3-642-86940-2Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: IX, 441

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computer Science, general, Mathematics, general

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