Matrix Inversion on GPUs

[kuruvinandan]

The paper http://www.hpca.uji.es/ficheros/remon/pdp11.pdf discusses how matrix inversion can be perfomed efficiently using Gauss-Jordan algorithm. It uses cuBLAS for L3 operations. They have reported impressive speedups and I hope they are talking only about single precision.

Any idea on how MAGMA might help in Inversion process? Should we go the LU way and solve for Identity Matrix (like TRSM)?
I assume we could make use of multi-GPUs for the LU...So, at least that should make it a bit easier...

Thanks,
Kuruvi...

[mgates3]

MAGMA has getri and potri for computing the inverse. These take the LU or Cholesky factors from getrf and potrf, respectively, and effectively do solves with the identity matrix, but are organized to compute in-place, overwriting the matrix A.

On the other hand, if your goal is to compute x=A^{-1} b, that is, to solve Ax=b, then using gesv (getrf and getrs) or posv (potrf and potrs) is both faster and more accurate than computing the explicit inverse and multiplying. We provide the capability to compute the inverse, but please use it only when the inverse itself is actually required.

-mark