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Symmetric successive over-relaxation

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

If the original matrix can be split into diagonal, lower and upper triangular as A = D + L + L T {\displaystyle A=D+L+L^{\mathsf {T}}} then the SSOR preconditioner matrix is defined as M = ( D + L ) D − 1 ( D + L ) T {\displaystyle M=(D+L)D^{-1}(D+L)^{\mathsf {T}}}

It can also be parametrised by ω {\displaystyle \omega } as follows. M ( ω ) = ω 2 − ω ( 1 ω D + L ) D − 1 ( 1 ω D + L ) T {\displaystyle M(\omega )={\omega \over {2-\omega }}\left({1 \over \omega }D+L\right)D^{-1}\left({1 \over \omega }D+L\right)^{\mathsf {T}}}

See also

References

  1. Iterative methods at CFD-Online wiki
  2. SSOR preconditioning at Netlib


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