# 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 ${\displaystyle A=D+L+L^{T}}$ then the 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]

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