Separate HTML for Scripted Foil 38 Over Relaxation (SOR) and Relation to Jacobi and Gauss-Seidel

Basic HTML version of Foils prepared 8 November 1995

Foil 38 Over Relaxation (SOR) and Relation to Jacobi and Gauss-Seidel

From CPS615 Module on Iterative PDE Solvers CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox

Jacobi and Gauss Seidel give a formula for x(k+1) in terms of x(k) call this x(k+1)

Overrelaxation forms x(k+1) = w x(k+1) + (1-w)x(k)

Typically only 0 < w < 2 is sensible w < 1 is relaxation 1 < w < 2 is over relaxation

First consider relaxation for Jacobi x(k+1) = wx(k+1) + (1-w)x(k)

There is an iteration matrix

G=M-1 N which on diagonalization we called K
with G=PTKP and P an orthogonal matrix