RE: positive definite banded solution of Ax=b

Depending on the situation, you may want to try WSMP or MUMPS. WSMP has both serial and MPI-based parallel sparse direct solver for SPD or indefinite matrices. 
MUMPS is open-source MPI-based parallel multifrontal solver. My experience is that it will take WSMP (10 to 100) seconds to factorize a similar matrix you mentioned. And WSMP has a super-fast triangular solver. 

For WSMP
http://www-users.cs.umn.edu/~agupta/wsmp.html

for MUMPS
http://www.enseeiht.fr/lima/apo/MUMPS/

Lie-Quan Lee
Advanced Computations Department
Stanford Linear Accelerator Center


> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> On Behalf Of Leon Lever
> Sent: Wednesday, January 26, 2005 5:23 AM
> To: [email protected]
> Subject: MTL: positive definite banded solution of Ax=b
> 
> I'm writing code for a finite element solver for the poisson equation.
>  The problem I'm having is that I can't find a routine that will
> decompose my banded matrix effieciently. The equation is Ax=b to solve
> for x where A is a sysmmetric banded matrix.  I wish to decompose it
> once, and then solve for different vectors b many times.  The matrix
> is ~10,000x10,000 with a bandwidth of ~100.  The dense lu
> decomposittion for this will take about 56 hours by my reckoning.
> Please can someone let me know of a better way.
> 
> Leon.
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