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Topic: Condition number of matrices
Replies: 5   Last Post: Jul 5, 2006 3:36 PM

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Doug Schwarz

Posts: 171
Registered: 12/7/04
Re: Condition number of matrices
Posted: Jul 5, 2006 3:36 PM
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Toni Lassila <toni@nukespam.org> wrote:

> If you can do SVD,

Doing an SVD as an aid in solving a linear system is not very practical.

Lapack (maybe inherited from Linpack?) has a condition estimator which
implicitly assumes that solving A^{-1}x is cheap. This is true for dense
systems, if the matrix has already been factored. The factorization has
N^3 cost, the solution N^2, so wasting a couple of solutions is
acceptable.

You can probably do the same thing for sparse matrices, if you use a
direct solver.

The remaining, though unfortunately rather important case, is sparse
systems and iterative methods. There, you construct your Hessenberg
matrix during the iteration process, and estimate its singular or eigen
values.

Victor.
--
Victor Eijkhout -- eijkhout at tacc utexas edu
ph: 512 471 5809



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