Separate HTML for Scripted Foil 39 Over Relaxation Eigenvalues and Matrices for Jacobi Iteration

Basic HTML version of Foils prepared 8 November 1995

Foil 39 Over Relaxation Eigenvalues and Matrices for Jacobi Iteration

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

The iteration matrices are related by

GJOR(w) = wGJ + (1-w )I

where I is the identity matrix and subscript JOR stands for Jacobi Over Relaxation

This relation is still true after diagonalization and is preserved for eigenvalues

lJOR(w) = wlJ + (1-w)

We need to look at those values of lJOR which are largest and smallest

These are:

lJOR|max = 1- p2/2N2 = 1- e

lJOR|min = -1+ p2/2N2 = -1+ e