topic Hi, in Intel® oneAPI Math Kernel Library

Linear System Solving For Tiny Matrix

Gianluca_G_1 — Thu, 20 Apr 2017 09:36:44 GMT

We are looking for to solve Linear Systems of tiny complex matrix like 10x10 in a very fast way.

We would like to use iterative methods because we have to solve a sequence with about 100 linear systems and solution of each system is a very good initial conditions for next system.

We've verified the direct solution method in the last MKL 2017 Update 2 but the speed is not enough.
I believe iterative methods could be the right solution.

What do you suggest?

Thank you

Gianluca

Hi,

Alexander_K_Intel2 — Thu, 20 Apr 2017 11:07:23 GMT

Hi,

Quick question - is your system sparse or dense?

Thanks,

Alex

System is dense up to size

Gianluca_G_1 — Thu, 20 Apr 2017 13:30:18 GMT

System is dense up to size 4x4 and sparse for bigger size systems

if your systems don't change

Alexander_K_Intel2 — Thu, 20 Apr 2017 14:07:13 GMT

if your systems don't change significantly from system to system I suggest to factorize first system and further use it's factorization as preconditioner for further systems. For sparse system you just need to call pardiso solver with phase 33 and set new matrix as input parameter. For dense you can implement simple iterative solver and use dgetrs functionality for preconditioner handle

Thanks,

Alex