The question is that simple. It is in the subject.

Why the name "relaxation" in the SOR Gauss-Seidel iterative method?

I have googled for it without luck.

Moreover, when $\omega$ is used in Gauss-Seidel is named "relaxation" and when $\omega$ is used in Jacboi is named: "weight" weighted Jacobi method

So, something got to be special about Gauss-Seidel to deserve such a name.

I observed that there is a "relaxation" technique explained in this thesis back from 1948. I do not see a connection between relaxation in that context of mechanics (PDEs) and the relaxation asked here which is in the context of linear systems such as Jacobi and Gauss-Seidel. Hence, I do not consider this as a duplicate questions.


  • $\begingroup$ @Moo : Thanks for your input. I downloaded David Young thesis. Very interesting and helpful. However I scanned through the introduction and could not find why the word "relaxation" is in the SOR abbreviation. Relaxation is a psychological term. What exactly does it have to do with relaxation of an equation? Relaxing what? I do not need to understand what it does (I think I know that). I want to understand where that word came from? Somebody was the first to use that word and it must have an explanation. Thanks. $\endgroup$ – Herman Jaramillo Jan 30 at 17:39
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    $\begingroup$ Possible duplicate of Why some linear iterative methods for linear system are also called "relaxation" methods? $\endgroup$ – Carl Christian Jan 30 at 20:20
  • $\begingroup$ Maybe because it’s related to functional minimization (energy norm of the error) along the coordinate directions $\endgroup$ – VorKir Feb 3 at 6:10

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