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Persistent URL http://purl.org/net/epubs/work/58276113
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Record Id 58276113
Title On incomplete Cholesky factorizations in half precision arithmetic
Abstract Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner is challenging. A resurgence of interest in using low precision arithmetic makes the search for robustness more important and more challenging. In this paper, we focus on symmetric positive definite problems and explore a number of approaches for preventing and handling breakdowns: prescaling of the system matrix, a look-ahead strategy to anticipate break down as early as possible, the use of global shifts, and a modification of an idea developed in the field of numerical optimization for the complete Cholesky factorization of dense matrices. Our numerical simulations target highly ill-conditioned sparse linear systems with the goal of computing the factors in half precision arithmetic and then achieving double precision accuracy using mixed precision refinement. We also consider the often overlooked issue of growth in the sizes of entries in the factors that can occur when using any precision and can render the computed factors ineffective as preconditioners.
Organisation STFC , SCI-COMP
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Language English (EN)
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Preprint STFC Preprints STFC-P-2024-002, Numer Algorithms STFC, 2024. STFC-P-2024-002.pdf 2024