Symmetric successive over-relaxation

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

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