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