Strategy for finding optimal omega in SOR method

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Tarek Hajj Shehadi 2021-8-14

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https://ww2.mathworks.cn/matlabcentral/answers/898142-strategy-for-finding-optimal-omega-in-sor-method

编辑： Tarek Hajj Shehadi 2021-8-14

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?