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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 Inst., Techn. Univ., 8 München 2, Deutschland

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Editors:
  1. F. L. Bauer

    1. Mathematisches Inst., Techn. Univ., 8 München 2, Deutschland

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Part of the book series: Handbook for Automatic Computation (HDBKAUCO, volume 2)

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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

Authors, Editors and Affiliations

  • Mathematisches Inst., Techn. Univ., 8 München 2, Deutschland

    F. L. Bauer, C. Reinsch

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

    J. H. Wilkinson

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