Basic HTML version of Foils prepared March 15 00

Foil 7 Formalism for Iterative Methods

From Collection of Extra Foils for CPS615 PDE Iterative Solution Discussion CPS615 Spring Semester 00 -- March 00. by Geoffrey C. Fox
Generic Iteration Strategy is to split matrix
  • A = M-N
  • so that it is much easier to invert M than A and in particular that inverting M can exploit zero structure of A
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 for given A and b
We must ensure that Iteration (*) converges and we naturally prefer that it converges fast!

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