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 $A=D+L+L^{\mathsf {T}}$ then the SSOR preconditioner matrix is defined as $M=(D+L)D^{-1}(D+L)^{\mathsf {T}}$

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

References

^ Iterative methods at CFD-Online wiki
^ SSOR preconditioning at Netlib

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[1] Iterative methods at CFD-Online wiki

[2] SSOR preconditioning at Netlib

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@@ Line 2: / Line 2: @@
 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 the 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^\mathsf{T}</math> then the SSOR preconditioner matrix is defined as
 <math display="block">M=(D+L) D^{-1} (D+L)^\mathsf{T}</math>

Revision as of 22:24, 18 October 2022

See also

References