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Re: [Help-gsl] solving linear system with large matrices

From: Paulo Jabardo
Subject: Re: [Help-gsl] solving linear system with large matrices
Date: Thu, 8 Mar 2007 15:06:03 -0300 (ART)

I recommend using LAPACK ( or
clapack (C interface).

The function you are looking for is 

dpbtrf  (cholesky decomposition)
dpbtrs  (uses the cholesky decomposition to solve the
linear system)

It does a Cholesky decomposition for banded matrices
(any bandwidth).

If you have any problems using these functions email
me and I can try to help you.

--- Jan Ehrhardt <address@hidden>

> Hello,
> I want to solve a linear system Ax=b, where A is
> symmetric, positive 
> definite square matrix.
> However, the size of the  matrix is very large:
> approx. 65000x65000 or 
> larger so an allocation
> of the whole matrix will fail. A is a tridiagonal
> matrix with two side 
> diagonal entries, all other entries are zero.
> So the structure is like
> (xx000x00000)
> (xxx000x0000)
> (0xxx000x000)
> (00xxx000x00)
> (000xxx000x0)
> (x000xxx000x)
> (0x000xxx000)
> but squared and much larger. I think a cholesky
> decomposition should 
> work to solve the system, but how can
> I allocate and store the matrix?
> I gsl is not able to handle such large matrices, are
> there other 
> possible solutions/libraries?
> Thanks.
> Jan
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