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Systems of Linear Equations

  • Chapter
Introduction to Numerical Analysis

Abstract

In this chapter direct methods for solving systems of linear equations

$$ Ax = b,A = \left[ \begin{array}{l} {a_{11}}...{a_{1n}}\\ \vdots \quad \quad \vdots \\ {a_{n1}}... \end{array} \right],b = \left[ \begin{array}{l} {b_1}\\ \vdots \\ {b_n} \end{array} \right] $$

will be presented. Here A is a given n × n matrix, and b is a given vector. We assume in addition that A and b are real, although this restriction is inessential in most of the methods. In contrast to the iterative methods (Chapter 8), the direct methods discussed here produce the solution in finitely many steps, assuming computations without roundoff errors.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg am Hubland, 8700, Würzburg, Federal Republic of Germany

    J. Stoer

  2. Institut für Mathematik, Technische Universität, 8000, München, Federal Republic of Germany

    R. Bulirsch

Authors
  1. J. Stoer
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  2. R. Bulirsch
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© 1980 Springer Science+Business Media New York

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Stoer, J., Bulirsch, R. (1980). Systems of Linear Equations. In: Introduction to Numerical Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5592-3_4

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  • DOI: https://doi.org/10.1007/978-1-4757-5592-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-5594-7

  • Online ISBN: 978-1-4757-5592-3

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