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Re: generalized eigenvectors [message #30222]

Tue, 16 April 2002 03:48

Randall Skelton
Messages: 169
Registered: October 2000

Senior Member

On Mon, 15 Apr 2002, Ralf Flicker wrote:

> In working on large sparse arrays it has become crucial to make the
> SVD more efficient than O(n^3), but that seems to be easier said
> than done. Do you know of an efficient implementation of the Laczos
> bidiagonalization with selective reorthogonalization? I have not
> been able to accomplish it - with complete, explicit
> reorthogonalization it actually gets even worse than O(n^3).

I have had this same problem in the past when attempting to solve large
Jacobian matrices. I haven't tried to implement the algorithm you
described, but I have definitely thought about trying it. I probably
won't get back to working on my code that relies on SVD for another month
or so but I seem to recall that the SVD was near the top of my "need to
optimize" list. Sorry I can't be of more help but at the moment CPU
cycles are cheaper than my time is... If you find anything in the mean
time, please post it!

> More to the point, has anyone _ever_ managed to bring down the SVD
> significantly below O(n^3) for sparse arrays? Pointers and
> suggestions welcome.

You may want to look at http://www.nersc.gov/research/SIMON/trlan.html and
the links therein. Unfortunately, the code is f90 so you'll need a
compiler as well as the BLAS and LAPACK libraries. If (read: when) I get
around to needing this, I will probably write a set of C DLM wrappers
around the public f90 functions.

Cheers,
Randall

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[Message index]

		Re: generalized eigenvectors By: Randall Skelton on Tue, 16 April 2002 03:48
		Re: generalized eigenvectors By: the_cacc on Tue, 16 April 2002 02:57
		Re: generalized eigenvectors By: Ralf Flicker on Mon, 15 April 2002 14:54
		Re: generalized eigenvectors By: Randall Skelton on Mon, 15 April 2002 14:29
		Re: generalized eigenvectors By: hradilv.nospam on Mon, 15 April 2002 08:36
		Re: generalized eigenvectors By: mvukovic on Tue, 16 April 2002 08:11
		Re: generalized eigenvectors By: Ralf Flicker on Wed, 17 April 2002 16:57

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