The open archive for STFC research publications

Full Record Details

Persistent URL http://purl.org/net/epubs/work/54056303
Record Status Checked
Record Id 54056303
Title Algebraic preconditioning in low precision works
Abstract The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for mixed precision variants of iterative refinement, with the emphasis so far being mainly on dense systems. We consider the iterative solution of large sparse systems using algebraic preconditioners. The focus is on the robust computation of incomplete factorization preconditioners in half precision arithmetic and employing them to solve symmetric positive definite systems to higher precision accuracy; however, the proposed ideas can be applied more generally. Even for well-scaled problems, incomplete factorizations can break down because of small entries on the diagonal. When using half precision arithmetic, overflows are an additional potential source of breakdown. We examine how breakdowns can be avoided and we implement our strategies within new half precision Fortran sparse incomplete Cholesky factorization software. Results are reported for a range of problems from practical applications. These demonstrate that, even for highly ill-conditioned problems, half precision preconditioners can replace double precision preconditioners, although unsurprisingly this can be at the cost of additional iterations of a Krylov solver.
Organisation STFC , SCI-COMP
Funding Information
Related Research Object(s):
Licence Information:
Language English (EN)
Type Details URI(s) Local file(s) Year
Preprint STFC Preprints STFC-P-2023-002, ACM Trans Math Software 2023. STFC-P-2023-002.pdf 2023