BLR compression solver gives wrong result about strumpack HOT 2 OPEN

Dear Dimitar,

My apologies for the delay. I tried your code, with the matrix you sent. And indeed the results seem wrong.

I believe the problem is a numerical issue. MKL dgesv performs partial pivoting, it looks for the largest element in each column, and uses that element as the pivot. But in BLR, we only look for the largest element in the column within the diagonal block.
I think for this matrix, this restricted pivoting might not be sufficient.
We could implement another variant of the BLR compression and factorization algorithm that is more numerically stable, I will discuss this with my collaborators.
Another thing you could try is to add a diagonal shift to the matrix, then compress and factor the shifted matrix and use that as a preconditioner.

We will try to fix the StructuredMatrix interface soon.

Pieter

from strumpack.

Thank you for the quick response.

Best Regards,
Dimitar Slavchev

from strumpack.