How can I solve linear equation system in parallel?

I am solving a linear equation system, , where A is a sparse square matrix and B is a sparse column vector. Before solving the system I use the command

dA = decomposition(A);

to return a decomposition of matrix A that I can use to solve the linear system more efficiently. In my case, it is Cholesky decomposition. Then I solve the system

x = dA\B;

and it works perfectly. My question is: how can I do it in parallel computing? or What is the best way to solve it in a cluster?

Answer 1

[John D'Errico]

You already are doing that!

That is, decomposition uses all of the cores you have available for large problems.

Watching my activity monitor while the decomposition was being done:

A = sprand(10000,10000,.001);

tic,DA= decomposition(A);toc
Elapsed time is 8.250635 seconds.

All 8 cores were being used. MATLAB does try to multithread many large computations, especially those involving linear algebra.

Answer 2

[Christine Tobler]

As John says, if you are using decomposition on one computer with several cores, the solver used already will use those cores if appropriate.

If you are working on a distributed system, and the matrix A is a distributed matrix, as of R2019b decomposition is also supported for this (see here).

[Heiko Weichelt]

Notice that decomposition of distributed arrays has a slightly limited subset for the underlying algorithms. Right now, sparse Cholesky, e.g., is not yet supported. Compare

>> help parallel.distributed.Decomposition.Type

and

>> help parallel.distributed.Decomposition

for the limitations.