Successive over-relaxation
= Successive over-relaxation
{title2=$\omega$}
{wiki}
= SOR
{c}
{synonym}
For a splitting $A=D+L+U$, <successive over-relaxation> updates
$$
(D+\omega L)x^{(k+1)}=[(1-\omega)D-\omega U]x^{(k)}+\omega b.
$$
It reduces to the <Gauss-Seidel method> at $\omega=1$. If $A$ is symmetric positive definite, the <Householder-John theorem> applies to $M=D/\omega+L$, $N=(1/\omega-1)D-U$, since $M^T+N=(2/\omega-1)D$ is positive definite for $0<\omega<2$.