Systems of Linear Equations

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


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.


Simplex Method Triangular Matrix Feasible Point Positive Definite Matrix Gaussian Elimination 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

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

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