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Re: st: inverting large, sparse matrices


From   Thomas Cornelißen <cornelissen@ewifo.uni-hannover.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: inverting large, sparse matrices
Date   Fri, 24 Nov 2006 16:07:30 +0100

"Pierre Azoulay" <pierre.azoulay@gmail.com> asks:
I am looking into the best strategy (and software package) to invert a
sparse positive definite 25,000 by 25,000 matrix. Is that something
feasible at all? I really have no idea. Does one need a supercomputer
to do this? Or would Stata/MP and 16 gigs of RAM do on a server do?
Would stata and matlab serve me equally well? Are there references to
look at? Are cholinv() and invsym() the right mata functions to look
at? Will these functions make use of the fact that the matrix is
sparse?

If I am not mistaken, neither -cholinv- nor -invsum- take into account the fact that the matrix is sparse. I think I understood from the literature that for large sparse system a preconditioned conjugate gradient algorithm (see for example Abowd, Creecy and Kramarz 2002) is a good solution, but I know of no implementation in Stata.
As far as I remember, the problem treated in Abowd, Creecy and Kramarz 2002 involves a higher dimension than 25,000 by 25,000.

Abowd J., Creecy R. and Kramarz F. (2002): "Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data', Technical Paper No. TP-2002-06, U.S. Census Bureau.

Thomas
-------------------------------------------------------------------------
Thomas Cornelissen
Institute of Empirical Economic Research
Leibniz Universität Hannover, Germany
cornelissen@ewifo.uni-hannover.de
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