Numerical Algebra

Numerical Algebra

1st Edition - January 28, 1978

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  • Author: John Todd
  • eBook ISBN: 9781483269412

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Basic Numerical Mathematics, Volume II: Numerical Algebra focuses on numerical algebra, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The existence of an orthogonal matrix which diagonalizes a real symmetric matrix is highlighted, and partitioned or block matrices are discussed, along with induced norms and inversion problems. Comprised of 12 chapters, this volume begins with an overview of the manipulation of vectors and matrices, followed by an analysis of induced norms. The reader is then introduced to the direct solution of the inversion problem, first in the context of theoretical arithmetic (that is, when round-off is disregarded) and second in the context of practical computation. Various methods of handling the characteristic value problems are also considered, together with several iterative methods for the solution of a system of linear equations. Two applications are described: the solution of a two-point boundary value problem and the solution of least squares curve fitting. The book concludes with an account of the singular value decomposition and pseudo-inverses. This monograph will be of interest to mathematicians and students of mathematics.

Table of Contents

  • Notations and Abbreviations


    Chapter 1. Manipulation of Vectors and Matrices

    Chapter 2. Norms of Vectors and Matrices

    Chapter 3. Induced Norms

    Chapter 4. The Inversion Problem I: Theoretical Arithmetic

    Chapter 5. The Inversion Problem II: Practical Computation

    Chapter 6. The Characteristic Value Problem — Generalities

    Chapter 7. The Power Method, Deflation, Inverse Iteration

    Chapter 8. Characteristic Values

    Chapter 9. Iterative Methods for the Solution of Systems Ax=b

    Chapter 10. Application: Solution of a Boundary Value Problem

    Chapter 11. Application: Least Squares Curve Fitting

    Chapter 12. Singular Value Decomposition and Pseudo-Inverses

    Solutions to Selected Problems

    Bibliographical Remarks


Product details

  • No. of pages: 216
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: January 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9781483269412

About the Author

John Todd

About the Editors

Ch. Blanc

A. Ghizzetti

P. Henrici

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