Basic HTML version of Foils prepared 8 November 1995

Foil 39 Over Relaxation Eigenvalues and Matrices for Jacobi Iteration

From Fox Presentation Fall 1995 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

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