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I'm trying to understand how the Jacobi method works and would appreciate a walk-through of the method with a very very simple example. In particular, I don't fully understand how one goes from the linear equation to a matrix.

Ah, my confusion is solved: http://en.wikipedia.org/wiki/System_of_linear_equations

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There are at least two methods named after Jacobi: one is a method for getting the eigenvalues of a symmetric matrix, and one is an iterative method for solving $\mathbf A\mathbf x=\mathbf b$. You'll need to be clear which one you're interested in. –  J. M. Sep 7 '11 at 10:33
    
I assume I'd be interested in the iterative method. For example, I'd like to solve TunkRank. –  lerninit Sep 7 '11 at 10:37
    
The example in Wikipedia looks particularly straightforward and simple. –  J. M. Sep 7 '11 at 11:15
    
@J.M. Please don't insult people who don't understand what you consider simple. –  lerninit Sep 7 '11 at 11:21
    
@J.M. For example, how was A derived from a linear equation? –  lerninit Sep 7 '11 at 11:22

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