From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Relaxation methods?
Date: 8 May 2000 10:18:13 GMT
Newsgroups: sci.math.num-analysis
Summary: [missing]

In article <3915BD4E.9E0AA4B2@compuserve.com>,
 Will Dwinnell <predictor@compuserve.com> writes:
|> I read an interesting article about relaxation methods some years ago,
|> and haven't seen much on them since.  Are they still in use?  Are there
|> better alternatives?
|> 
you mean SOR for linear systems? Of course these methods are still in use,
but not of much interest (although a lot of people continue to publish
papers on convergence conditions for modified , extended whatsover modifications
of that.) the reason is that true overrelaxation works badly with multigrid 
and these basic iterative methods are now used mainly as smoothers for multigrid
solvers for linear systems. On the other side, there is much interest in 
Krylow subspace methods, which are generalizations of the classical cg.
these work very well if combined with some good "preconditioner" 
(a simple linear transformation of the system which improves the distribution
of the iegenvalues of the matrix).
have a look at the very well written book of Demmel "applied numerical 
linear algebra"
published by SIAM.
hope that helps
peter