Symmetric successive over-relaxation

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 $A=D+L+L^{\mathsf {T}}$ 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.

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

See also

• Successive over-relaxation