symmetric successive over-relaxation

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In applied mathematics, symmetric successive over-relaxation (SSOR),[http://www.cfd-online.com/Wiki/Iterative_methods Iterative methods] at CFD-Online wiki is a preconditioner.

If the original matrix can be split into diagonal, lower and upper triangular as $A=D+L+L^\backslash mathsf\{T\}$ then the SSOR preconditioner matrix is defined as

$$M=(D+L)\; D^\{-1\}\; (D+L)^\backslash mathsf\{T\}$$

It can also be parametrised by $\backslash omega$ as follows.[http://www.netlib.org/linalg/html_templates/node58.html SSOR preconditioning] at Netlib

$$M(\backslash omega)=\{\backslash omega\backslash over\{2-\backslash omega\}\}\; \backslash left\; (\; \{1\backslash over\backslash omega\}\; D\; +\; L\; \backslash right\; )\; D^\{-1\}\; \backslash left\; (\; \{1\backslash over\backslash omega\}\; D\; +\; L\backslash right)^\backslash mathsf\{T\}$$