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- From: eijkhout@cupid.cs.utk.edu (Victor Eijkhout)
- Newsgroups: comp.lang.fortran
- Subject: Re: inverse matrix
- Date: 12 Jan 93 16:16:20
- Organization: /pearl/homes/eijkhout/.organization
- Lines: 40
- Message-ID: <EIJKHOUT.93Jan12161620@cupid.cs.utk.edu>
- References: <1993Jan8.201645.14915@news.eng.convex.com> <C0p5JD.M0L@news.udel.edu>
- <EIJKHOUT.93Jan11153758@cupid.cs.utk.edu> <C0pKup.vJ@news.udel.edu>
- NNTP-Posting-Host: cupid.cs.utk.edu
- In-reply-to: mccalpin@perelandra.cms.udel.edu's message of Mon, 11 Jan 1993 21:25:37 GMT
-
- In article <C0pKup.vJ@news.udel.edu> mccalpin@perelandra.cms.udel.edu (John D. McCalpin) writes:
-
- In article <EIJKHOUT.93Jan11153758@cupid.cs.utk.edu> eijkhout@cupid.cs.utk.edu (Victor Eijkhout) writes:
- >In article <C0p5JD.M0L@news.udel.edu> mccalpin@perelandra.cms.udel.edu (John D. McCalpin) writes:
- >
- > In article <1993Jan8.201645.14915@news.eng.convex.com> dodson@convex.COM (Dave Dodson) writes:
- > >I'd like to point out that it is almost never required or desirable to
- > >compute the inverse of a matrix.
- >
- > The direct use of the inverse matrix is generally the fastest way to
- > solve a dense system of equations with multiple, consecutive right-hand-sides
- > (as in a time-dependent fluid dynamics problem).
- >
- >Where do dense systems come from in fluid dynamics? Usually
- >differential equations (partial or otherwise) give sparse
- >matrices, and then calculating the inverse is at least a major
- >waste of space.
-
- The matrices are dense for spectral integration or differentiation
- using any basis functions except trig functions. The last time I
- checked, this was still the fastest way to solve separable Poisson-like
- equations using Chebyshev discretization, for example.
-
- But only on domains that are a Cartesian product of intervals, right?
- Or can you handle separable equations on arbitrarily shaped domains
- (Chessapeake bay?) this way?
-
- Dense matrices alse arise in the capacitance matrix method for solving
- the elliptic PDE's that often arise in fluid dynamics problems.
-
- Isn't that after eliminating most of a *sparse* matrix onto
- some subset of the variables (corresponding to an interior line
- in the domain) so that there is an outer problem that is sparse?
-
- John D. McCalpin
- --
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