Re: [boost] A possible GSOC 2011 proposal idea

Subject: Re: [boost] A possible GSOC 2011 proposal idea
From: Thomas Klimpel (Thomas.Klimpel_at_[hidden])
Date: 2011-03-21 10:04:11

Mathias Gaunard wrote:
> On 21/03/2011 12:00, Chad Seibert wrote:
> > If the Boost community thinks that
> > these are reasonable and I should forgo solving LP in favor of
> solving large
> > (>  100,000x100,000) LS, we can certainly discuss this. The following
> > algorithms are up for consideration:
> >
> > * LU decomposition for small matrices
> > * Iterative methods for large matrices, such as conjugate gradient
> >   for positive definite matrices
> 
> Doesn't LAPACK already do that?

LAPACK certainly does the small matrices part (note how Chad has defined "small").

The iterative methods for large matrices part seem a bit questionable to me in this context, because I see no reasons why the matrices should be positive definite, or have any other "guaranteed" property that would assure convergence of iterative methods. On the other hand, LP matrices often have few non-zero elements, so that sparse direct methods could be used when LAPACK is no longer appropriate. I think even an ILU preconditioner for an iterative method would still require methods related to these sparse direct methods. There are libraries for this, like umfpack, mumps, superLU and others. Sorry for being a bit sloopy here, but being more precise (and verifying that my answers are relatively correct) would cost me more time than I want to spend for this answer right now.

Regards,
Thomas