Strategy for finding optimal omega in SOR method

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Tarek Hajj Shehadi
Tarek Hajj Shehadi 2021-8-14
回答： nour 2024-6-27
I had written an algorithm that searches for the optimal weight parameter to be implemented in the successive-over relaxation (SOR) method which worked cleanly by vectorizing the interval and for each ω the spectral radius of the iteration matrix is computed.
However, I was advised not to use this approach for large sparse matrices as it is expensive to compute (the same way computing condition number of a large matrix is unfeasible) and rather use it as a demonstration tool. Therefore, I was wondering what strategy is the best to approximate the optimal weight parameter for large sparse systems () that would allow the best convergence of the SOR.
Furthermore, as a result of my question I was wondering if classical iterative stationary methods such as Jacobi, Gauss-Seidel, and the SOR are worthy to be used nowadays in dealing with large sparse systems or is the default preference Krylov methods?

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nour
nour 2024-6-27
A = [5 2 -1; 2 6 3; 1 4 -8];
b = [1; 2; 1];
x0 = [0; 0; 0];
e = 0.001;

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