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Systems of Linear Equations

  • Chapter
Introduction to Numerical Analysis

Part of the book series: Texts in Applied Mathematics ((TAM,volume 12))

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Abstract

In this chapter direct methods for solving systems of linear equations

$$Ax = b.A = \left[ {\begin{array}{*{20}{c}} {{a_{11}}}& \cdots &{{a_{{1_n}}}} \\ \vdots &{}& \vdots \\ {{a_{{n_1}}}}& \cdots &{{a_{nn}}} \end{array}} \right],b = \left[ {\begin{array}{*{20}{c}} {{b_1}} \\ \vdots \\ {{b_n}} \end{array}} \right]$$

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, Germany

    J. Stoer

  2. Institut für Mathematik, Technische Universität, 8000, München, Germany

    R. Bulirsch

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  1. J. Stoer
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  2. R. Bulirsch
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© 1993 Springer Science+Business Media New York

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Stoer, J., Bulirsch, R. (1993). Systems of Linear Equations. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2272-7_4

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  • DOI: https://doi.org/10.1007/978-1-4757-2272-7_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2274-1

  • Online ISBN: 978-1-4757-2272-7

  • eBook Packages: Springer Book Archive

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