my guess is that you need your matrix to be diagonally dominant
Jacobi method - Wikipedia, the free encyclopedia
I have been given an equation which does not converge when the jacobi method is applied to it:
The question I am having trouble with asks to re arrange it so that it will converge. I have been looking into it and am so far unable to see what approach I should take. Rather stupidly I began by ensuring the diagonal is zero, which (of course) produces nothing (NAN). All my other attempts have given a system which similarly does not converge.
I have been using to help provide insight to what form I need the matrix in, but it has not yet helped. This is quite urgent, so any help you can provide I would be grateful for.