# Systems of Linear Equations

• J. Stoer
• R. Bulirsch
Part of the Texts in Applied Mathematics book series (TAM, volume 12)

## 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.

## Keywords

Simplex Method Triangular Matrix Feasible Point Positive Definite Matrix Gaussian Elimination
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• J. Stoer
• 1
• R. Bulirsch
• 2
1. 1.Institut für Angewandte MathematikUniversität WürzburgWürzburgGermany
2. 2.Institut für MathematikTechnische UniversitätMünchenGermany