Over-relaxation

Let us rewrite G-s

The term in square brackets can be thought of as a correction to the current iterate, to produce a new iterate. Instead of taking 1 times this correction, we could correct with some other multiple of this correction

The multiplier is a relaxation parameter. Different choices of the relaxation parameter lead to different convergence rates. The "best" choice is highly problem-dependent. Some facts are useful:

1. If the diagonal entries are non-zero,
2. If A is symmetric, positive-definite, and , then SOR converges
3. If A is symmetric, positive-definite, tridiagonal, then , and the best choice is .