Talk:Jacobi method/Archive 1

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Archive 1

v.s. Gauss-Seidel

I don't agree that the difference in storage "is the most meaningful difference" between Jacobi and Gauss-Seidel. More important would be two facts: Gauss-Seidel is faster (it uses "more recent" information), but there are some cases when Jacobi converges and Gauss-Seidel doesn't (and vice-versa). Also important is the fact that Jacobi converges regardless of the row ordering of the matrix (and the corresponding linear system), while Gauss-Seidel depends on the ordering.

Also, after putting the algorithm into the common matrix forms (e.g. write A = D - L - U), it would be nice to compare it to Gauss-Seidel.

And mention of JOR (Jacobi Over Relaxation) would be nice.

Even better would be some data on flops required per iteration, some sample problems solved (e.g. how many iterations to reach a desired tolerance), and some analysis about the convergence rates (especially compared to other methods).

Lavaka 02:40, 18 September 2006 (UTC)

Algorithm

I find the algorithm presented too complicated, it contains 3 loops, why?

Either iterate a fixed number of times, then a simple for will do,
or if you want to use a sort of stopping criteria then a simple while of the sort:

while Error > TOL && loop<loopmax
end

will do. Oub (talk) 19:15, 23 January 2010 (UTC):

Unclear

This article is not so clear. Maybe further improvement is needed. —The preceding unsigned comment was added by 65.206.118.19 (talk • contribs) 20:02, 6 July 2006 (UTC)

Example

Is there any reason to decompose the remainder into upper and lower components? This unnecessarily complicates the example in my opinion.— Preceding unsigned comment added by 173.26.206.167 (talk) 23:16, 14 June 2011 (UTC)