On incomplete Cholesky factorizations in half precision arithmetic
<|reference_start|>On incomplete Cholesky factorizations in half precision arithmetic: 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 urgent and tougher. In this paper, we focus on symmetric positive definite problems and explore a number of approaches: 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.<|reference_end|>
@article{scott2024on,
    title={On incomplete Cholesky factorizations in half precision arithmetic},
    author={Jennifer Scott, Miroslav Tr{u}ma},
    journal={arXiv preprint arXiv:2403.13123},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.13123},
    primaryClass={math.NA cs.NA}
}