Separate HTML for Scripted Foil 41 Jacobi Relaxation for Over Relaxation Parameter w =1/2

Basic HTML version of Foils prepared 8 November 1995

Foil 41 Jacobi Relaxation for Over Relaxation Parameter w =1/2

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

For w=1/2, one has

x(k+1) =1/2[x(k) + x(k+1 ) ] where J denotes Pure Jacobi

and subscript JOR stands for Jacobi Over Relaxation again

This has "update" matrix in two dimensions

xpoint = 1/2 xpoint + 1/8 times x of four neighbors

We now "couple" even and odd grid points which were decoupled in original Jacobi

Corresponding eigenvalue of most rapidly varying eigenfunction is

now lJOR|min ~ 0

not lJOR|min ~ -1 as before