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  • © 1971

Handbook for Automatic Computation

Volume II: Linear Algebra

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 186)

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  • ISBN: 978-3-642-86940-2
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Table of contents (29 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-8
    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. Symmetric Decomposition of Positive Definite Band Matrices

      • R. S. Martin, J. H. Wilkinson
      Pages 50-56
    5. The Conjugate Gradient Method

      • T. Ginsburg
      Pages 57-69
    6. Solution of Real and Complex Systems of Linear Equations

      • H. J. Bowdler, R. S. Martin, G. Peters, J. H. Wilkinson
      Pages 93-110
    7. Linear Least Squares Solutions by Housholder Transformations

      • P. Businger, G. H. Golub
      Pages 111-118
    8. Singular Value Decomposition and Least Squares Solutions

      • G. H. Golub, C. Reinsch
      Pages 134-151
    9. 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
    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

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.

Keywords

  • ALGOL
  • Algol W
  • Calculation
  • Finite
  • Natural
  • algebra
  • algorithms
  • computer
  • eigenvalue problem
  • equation
  • numerical analysis
  • programming

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: 978-3-642-86942-6

  • eBook ISBN: 978-3-642-86940-2

  • 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, Mathematics

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-86940-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)