Linear System Solving For Tiny Matrix

[Gianluca_G_1]

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

[Alexander_K_Intel2]

Hi,

Quick question - is your system sparse or dense?

Thanks,

Alex

[Gianluca_G_1]

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

[Alexander_K_Intel2]

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