Successive Over-Relaxation Algorithm

Successive over-relaxation is an iterative algorithm for solving a system of linear equations, built as a variant of the older Gauss-Seidel method that converges to the answer faster. It works by applying the same basic Gauss-Seidel updating rule but then overshooting each new estimate slightly, weighted by a relaxation factor greater than one, so successive iterations move toward the true solution more aggressively than plain Gauss-Seidel would while still eventually settling to the correct answer for suitable choices of that factor. David Young and Stanley Frankel independently devised the method in 1950, specifically to make linear system solving practical to automate on the newly available digital computers of the time, building on earlier, hand-calculation-era over-relaxation ideas from Lewis Fry Richardson and R. V. Southwell.