Symmetric successive over-relaxation: Difference between revisions

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In applied mathematics, symmetric successive over-relaxation (SSOR),^[1] is a preconditioner.

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

M=(D+L)D^{-1}(D+L)^{T}

It can also be parametrised by $\omega$ as follows.^[2]

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

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 In applied mathematics, '''symmetric successive over-relaxation (SSOR)''',<ref>[http://www.cfd-online.com/Wiki/Iterative_methods Iterative methods] at CFD-Online wiki</ref> is a [[preconditioner]].
-If the original matrix can be [[Matrix splitting|split]] into diagonal, lower and upper triangular as <math>A=D+L+L^T</math> then SSOR preconditioner matrix is defined as
+If the original matrix can be [[Matrix splitting|split]] into diagonal, lower and upper triangular as <math>A=D+L+L^T</math> then the SSOR preconditioner matrix is defined as
 : <math>M=(D+L) D^{-1} (D+L)^T</math>