# Symmetric successive overrelaxation

In applied mathematics, symmetric successive overrelaxation (SSOR),[1] is a preconditioner.

If the original matrix can be split into diagonal, lower and upper tridiagonal as ${\displaystyle A=D+L+L^{T}}$ then SSOR preconditioner matrix is defined as

${\displaystyle M=(D+L)D^{-1}(D+L)^{T}}$

It can also be parametrised by ${\displaystyle \omega }$ as follows.[2]

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