Umut Tabak <[email protected]> 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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