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Can anyone explain to me the SOR Method for finding the root(s) of a function? Its supposedly very similar to the Gauss-Seidel method.

The Gauss-Seidel method, from my understanding, is similar to the Jacobi method such that we start with an initial guess (e.g. $x = \left [0,0,0 \right ]$ for a $3 \times 3$ matrix) and solve for $x_1,x_2,\dots,x_k$. Then use the values for $x_1\dots x_k$ from $x = \left [0,0,0 \right ]$ to find the next iteration of values. However, with the Gauss-Seidel method, we immediately use the updated/new $x$'s when going through the iterations instead of using the value found in the previous iteration.

So now, the SOR method? How does it differ?

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  • $\begingroup$ Similarly to Gauss-Seidel, SOR uses the components of the solution vectors updated in the current sweep. You can see it clearly from the formula at the end of the Formulation section on its wiki page: en.wikipedia.org/wiki/Successive_over-relaxation $\endgroup$ – Algebraic Pavel Feb 18 '14 at 16:35
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Have a look at
http://www-solar.mcs.st-andrews.ac.uk/~clare/Lectures/num-analysis/Numan_chap2.pdf
The explanations are very clear and you will find a clear comparison of the different methods.

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