Symmetric successive over-relaxation explained

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

then the SSOR preconditioner matrix is defined as$$M=(D+L)\; D^\; (D+L)^\backslash mathsf$$

It can also be parametrised by

as follows.^[2] $$M(\backslash omega)=\; \backslash left\; (D\; +\; L\; \backslash right)\; D^\; \backslash left\; (D\; +\; L\backslash right)^\backslash mathsf$$

See also

• Successive over-relaxation

References

1. http://www.cfd-online.com/Wiki/Iterative_methods Iterative methods
2. http://www.netlib.org/linalg/html_templates/node58.html SSOR preconditioning