[petsc-users] any good references on matrix scaling

Jed Brown jedbrown at mcs.anl.gov
Thu Sep 12 14:00:10 CDT 2013

Umut Tabak <u.tabak at tudelft.nl> writes:

> Dear all,
> I am looking for some references for matrix scaling where I would like 
> to improve the conditioning of a block representation such as
> A C
> C^T B
> where the terms in A and B blocks are of very different orders, such as 
> A is of 1e+8 and B for instance is of order 1e-4 . The ratios can get 
> even worse but not better on the problems I tried.

I recommend non-dimensionalizing (i.e., choosing units) so the system is
better scaled.

> I am trying have an overview for some cheap conditioning approaches for 
> this problem.

Most preconditioners use the diagonal enough to fix the disparate
scales.  If you are using full-space iteration with PCFIELDSPLIT, you'll
likely have to scale the variables first.  You can always use Schur
complement reduction.
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