A Mixed-Precision Model for Matrix-Splitting Methods
Abstract
The performance of stationary iterative methods is memory-bound, due to the low arithmetic intensity. So, we propose a mixed-precision technique to reduce the amount of data movement in matrix-splitting iterative methods. We demonstrate both theoretically and experimentally that this technique will generally converge at a similar rate as an exact-precision iteration, depending on the precision used and the conditioning of the M matrix. Furthermore, we demonstrate that iterative refinement can be used to refine the solution to full double-precision accuracy. Using this approach, we mixed half and double precision to achieve an average speedup over uniform double precision of 1.60× for scalar and block Jacobi and 1.25× for scalar and block Gauss-Seidel. Furthermore, we reduced the precision in the SSOR iteration used by OVERFLOW, a NASA code for compressible fluid dynamics simulations, and achieved a 1.14× speedup to the overall application.
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BibTeX
@misc{lindquist2026mixedprecision,
title = {{A Mixed-Precision Model for Matrix-Splitting Methods}},
author = {Neil Lindquist and David Appelhans and Chales W. Jackson and Joseph M. Derlaga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06414},
eprint = {2610.06414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06414},
}
RIS
TY - UNPB
TI - A Mixed-Precision Model for Matrix-Splitting Methods
AU - Neil Lindquist
AU - David Appelhans
AU - Chales W. Jackson
AU - Joseph M. Derlaga
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06414
UR - https://arxiv.org/abs/2610.06414
AB - The performance of stationary iterative methods is memory-bound, due to the low arithmetic intensity. So, we propose a mixed-precision technique to reduce the amount of data movement in matrix-splitting iterative methods. We demonstrate both theoretically and experimentally that this technique will generally converge at a similar rate as an exact-precision iteration, depending on the precision used and the conditioning of the M matrix. Furthermore, we demonstrate that iterative refinement can be used to refine the solution to full double-precision accuracy. Using this approach, we mixed half and double precision to achieve an average speedup over uniform double precision of 1.60× for scalar and block Jacobi and 1.25× for scalar and block Gauss-Seidel. Furthermore, we reduced the precision in the SSOR iteration used by OVERFLOW, a NASA code for compressible fluid dynamics simulations, and achieved a 1.14× speedup to the overall application.
ER -