Formalism for Iterative Methods
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!