Separate HTML for Scripted Foil 22 General Iteration Matrix Splitting and Preconditioning

Basic HTML version of Foils prepared 8 November 1995

Foil 22 General Iteration Matrix Splitting and Preconditioning

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

Generic Iteration

Split A = M-N Ax = b implies Mx = Nx + b So write Mxk = Nx(k-1) + b
All iteration methods have this form for different choices of M, N, A and b
- One can change A and b by preconditioning
- M1-1AM2-1M2x =M1-1 b is same equation as before for any choice of matrices M1 and M2
All these choices are designed to accelerate convergence of iterative methods