Mixed precision GMRES-based iterative refinement with recycling

Oktay, Eda, and Carson, Erin. "Mixed precision GMRES-based iterative refinement with recycling." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 149-162. <http://eudml.org/doc/299005>.

@inProceedings{Oktay2023,
abstract = {With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems $Ax=b$ have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations, of a Krylov subspace method into a mixed precision GMRES-based iterative refinement solver. The insight is that in each refinement step, we call preconditioned GMRES on a linear system with the same coefficient matrix $A$. In this way, the GMRES solves in subsequent refinement steps can be accelerated by recycling information obtained from previous steps. We perform numerical experiments on various random dense problems, Toeplitz problems, and problems from real applications, which confirm the benefits of the recycling approach.},
author = {Oktay, Eda, Carson, Erin},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {GMRES; iterative refinement; mixed precision; recycling},
location = {Prague},
pages = {149-162},
publisher = {Institute of Mathematics CAS},
title = {Mixed precision GMRES-based iterative refinement with recycling},
url = {http://eudml.org/doc/299005},
year = {2023},
}

TY - CLSWK
AU - Oktay, Eda
AU - Carson, Erin
TI - Mixed precision GMRES-based iterative refinement with recycling
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 149
EP - 162
AB - With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems $Ax=b$ have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations, of a Krylov subspace method into a mixed precision GMRES-based iterative refinement solver. The insight is that in each refinement step, we call preconditioned GMRES on a linear system with the same coefficient matrix $A$. In this way, the GMRES solves in subsequent refinement steps can be accelerated by recycling information obtained from previous steps. We perform numerical experiments on various random dense problems, Toeplitz problems, and problems from real applications, which confirm the benefits of the recycling approach.
KW - GMRES; iterative refinement; mixed precision; recycling
UR - http://eudml.org/doc/299005
ER -