Ax = b for a lot of different b‘s

Hello,

I have a system of equation Ax = b, where A is very large (n = 3e5 - 8e5) and sparse coefficient matrix, b is source term and x is the solution. Of course it's not a problem to solve such a problem in MATLAB, however I have to solve Ax = b for a lot of different b‘s without any change in the coefficient matrix A. The inversion of the matrix A take so long, that it is faster to solve the problem for each new b vector separately using an iterative solver. Unfortunately it is still way too slow, so I'm looking for a way how to speed it up.

Does anybody know, how to improve the performance?

Thank you for help!

Answer 1

[Matt J]

Neither direct inversion of A, nor iterative methods are required. Just create a matrix B whose columns are the different b. Then do

    X=A\B

Each column X(:,i) will be the solution for the corresponding b.

[Jan]

+1: This looks trivial, but it is such useful!

[David Kusnirak]

well it really helps! I have lost some control, e.g. precision, parralelization or preconditioning, but it works just fine. I wonder how good can MATLAB handle such huge datasets in this manner..

[Matt J]

well it really helps! I have lost some control, e.g. precision, parralelization or preconditioning

Not sure why you feel you've lost precision or why you think pre-conditioning matters when you're using a non-iterative method. It's true you have no control over the parallelization, but parallelization is done for you internally by MLDIVIDE.

[David Kusnirak]

It works just fine as I said, thanks for help. The precision is far behind my tolerance treshold I used to use with the iterative solver, and of course preconditioning is not necessary now. I just felt better to have more response about what's going on, as the mldivide is somehow just a 'blackbox' for me.