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Next: 2.2.2 Householder Transformation Up: 2.2 Exact Methods Previous: 2.2 Exact Methods

2.2.1 Gauss Elimination and Back Substitution


$\displaystyle \left( \begin{array}{ccccc} a_{11} & a_{12} & . & . & a_{1N} \\ ... ...ot \left( \begin{array}{c} x_{1} \\ . \\ .\\ . \\ x_{N} \end{array} \right)$ $\textstyle =$ $\displaystyle \left( \begin{array}{c} b_{1} \\ . \\ .\\ . \\ b_{N} \end{array} \right)$  

Convert this to triangular form:

$\displaystyle \left( \begin{array}{ccccc} a_{11}'& a_{12}' & . & . & . \\ 0 & ... ...ot \left( \begin{array}{c} x_{1} \\ . \\ .\\ . \\ x_{N} \end{array} \right)$ $\textstyle =$ $\displaystyle \left( \begin{array}{c} b_{1}' \\ . \\ .\\ . \\ b_{N}' \end{array} \right)$  



Then solve the system by Back Substitution.
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001