Basic HTML version of Foils prepared 8 November 1995

Foil 22 General Iteration Matrix Splitting and Preconditioning

From Fox Presentation Fall 1995 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

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