Talk:Successive over-relaxation

Index k
The algorighm section has a k loop and also a superscript k. I don't think these k's are related, but I'm not sure. If they are not related, I think we should choose a different variable for the loop.Epachamo 00:26, 3 March 2006 (UTC)


 * They are related: $$\phi^{(k)}$$ denotes the guess for the solution in the kth iteration. Of course, in a real implementation, one wouldn't keep all the previous &phi; in memory, but only the current guess. -- Jitse Niesen (talk) 00:37, 3 March 2006 (UTC)


 * That makes sense. Thanks! Epachamo 05:39, 3 March 2006 (UTC)

The first $$\phi_j^{(k+1)}$$ in the pseudocode should just be $$\phi_j^{(k)}$$. I don't see how you can call the $$(k+1)'th$$ term when you haven't calculated it yet.

In any case, I used the alteration I have suggested in MATLAB, and it works.

Bradridder (talk) 05:34, 4 September 2009 (UTC)

Hm. Actually, I'm not sure now. I have looked all over the internet, Numerical Recipes in C, and another numerical analysis book, and it does appear that the previous version was correct.

As per how that works exactly in practice, I am not sure.

I will change the first $$\phi_j^{(k)}$$ back to $$\phi_j^{(k+1)}$$. Bradridder (talk) 03:39, 5 September 2009 (UTC)

Time Complexity
Can anyone post the time complexity of SOR in detail —Preceding unsigned comment added by 203.199.213.66 (talk) 11:17, 26 May 2009 (UTC)

Since the number of iterations is a complicated function of spectrum this can not be predicted in general. The complexity of one iteration can easily be given as 2*nz where nz is the number of nonzeros in the matrix. Eijkhout (talk) 19:55, 1 December 2010 (UTC)

Attribution
Jack Dongarra's name was only attached to the reference because he uploaded it to netlib. (I'm one of the authors. I know.) —Preceding unsigned comment added by Eijkhout (talk • contribs) 19:53, 1 December 2010 (UTC)

"Main article Richardson Extrapolation"?
In the section Other applications of the method it says that Richardson extrapolation is the main article for the section. I don't see the connection between the section and Richardson extrapolation; can someone please explain to me what they have to do with each other? —Kri (talk) 22:04, 4 September 2012 (UTC)

Algorithm Incorrect
Both SOR and Gauss-Seidel articles have incorrect algorithms. The Gauss-Seidel article is just the Jacobi method and the algorithm in the SOR article is extrapolated Jacobi. You can easily tell because SOR/Gauss-Seidel should have two inner loops, one that goes from 1 to i-1 and another that goes from i+1 to n. — Preceding unsigned comment added by 98.27.130.28 (talk) 17:51, 15 August 2013 (UTC)

Needs more SSOR
Hi, I think the description for SSOR is a bit lacking, no examples and some of the variables like gamma are not defined. --Frozenport (talk) 09:36, 12 December 2013 (UTC)

Relaxation parameter
"the system of (...) may be rewritten as" for any $\omega > 1$ this statement is a bit confusing with the following statement where one reads that for convergence, it is necessary for $\omega$ to be $]0,2[$. As far as I'm aware, the decomposition holds for any $\omega \neq 0$ and a necessary condition for convergence is indeed $|\omega -1|<1$ which for the real case amounts to $\omega\in]0,2[$. I would suggest that someone more expert than me on these questions reviews this. The following paper: http://www.sciencedirect.com/science/article/pii/S0377042700004039 may be a good reference. Thibaut Lienart (talk) 16:47, 17 March 2015 (UTC)

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Formula for Symmetric Successive over-relaxation
It seems to me that the formula for the preconditioner in the ssor section is incorrect, I think it should be


 * $$P=\left(\frac{D}{\omega}+L\right)\frac{1}{2-\omega}D^{-1}\left(\frac{D}{\omega}+U\right),$$ or
 * $$P=\left(\frac{D}{\omega}+L\right)\frac{1}{2-\omega}D^{-1}\left(\frac{D}{\omega}+L\right)^T,$$ or
 * $$P=\left(\frac{D}{\omega}+U\right)\frac{1}{2-\omega}D^{-1}\left(\frac{D}{\omega}+U\right)^T,$$ or
 * $$P=\left(\frac{D}{\omega}+U\right)\frac{1}{2-\omega}D^{-1}\left(\frac{D}{\omega}+L\right),$$ but not


 * $$P=\left(\frac{D}{\omega}+L\right)\frac{1}{2-\omega}D^{-1}\left(\frac{D}{\omega}+U\right)^T,$$ the way it is now. As it is written now, the preconditioner is not symmetric.  If I am correct, let me know and I will make the change to the first display I wrote.  — Preceding unsigned comment added by 2601:404:CF80:1BC4:4DB:96AC:65CD:5042 (talk) 14:51, 18 October 2018 (UTC)


 * Agreed, so I've gone ahead and fixed the formula. 95.144.76.161 (talk) 13:30, 28 December 2018 (UTC)

Choice of the example
I wonder about the choice of the example. The coefficient matrix is not diagonally dominant, it is not even symmetric and positive definite. For some reason it converges fine for the chosen $$\omega = 0.5$$, although very slowly. — Preceding unsigned comment added by Mhx (talk • contribs) 06:45, 14 August 2021 (UTC)