Separate Focus 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

1	The iteration matrices are related by
2	GJOR(w) = wGJ + (1-w )I
3	where I is the identity matrix and subscript JOR stands for Jacobi Over Relaxation
4	This relation is still true after diagonalization and is preserved for eigenvalues
5	lJOR(w) = wlJ + (1-w)
6	We need to look at those values of lJOR which are largest and smallest
7	These are:
8	lJOR\|max = 1- p2/2N2 = 1- e
9	lJOR\|min = -1+ p2/2N2 = -1+ e