Separate HTML for Scripted Foil 40 Jacobi Iteration Eigenvalues as a function of Over Relaxation Parameter

Basic HTML version of Foils prepared 8 November 1995

Foil 40 Jacobi Iteration Eigenvalues as a function of Over Relaxation Parameter

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

lJOR|max(w) = 1 - ew

This is decreased in absolute value for w > 1, increased for w < 1

lJOR|min(w) = 1+ we - 2w

This is just the opposite
Increased for w > 1, decreased for w < 1

The best value of w is w = 1 i.e. Best is Original Jacobi iteration as one must minimize the maximum over all values of eigenvalue moduli |l| and for Jacobi one canNOT use overrelaxation