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Thread: Jacobi Method rearrangement of linear system (help!)

  1. #1
    Apr 2009

    Jacobi Method rearrangement of linear system (help!)

    I have been given an equation which does not converge when the jacobi method is applied to it:
    $\displaystyle \begin{pmatrix}1&-1&0&0&8&-2\\0&2&10&1&2&-1\\1&5&-1&2&0&1\\-1&0&1&1&0&-4\\-2&-1&0&0&1&0\\0&-2&0&4&0&1\end{pmatrix}$

    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 $\displaystyle x^{k} = -D^{-1}(L+U)x^{k-1}+D^{-1}b$ 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.
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  2. #2
    Junior Member
    Nov 2009
    my guess is that you need your matrix to be diagonally dominant
    Jacobi method - Wikipedia, the free encyclopedia
    good luck!
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