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

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

See also

• Successive over-relaxation