A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

• DOI: 10.1177/10943420211003313
• Publication Date: 2021-03-19T10:02:38Z
• Authors: Ahmad Abdelfattah; Hartwig Anzt; Erik G Boman; Erin Carson; Terry Cojean; Jack Dongarra; Alyson Fox; Mark Gates; Nicholas J Higham; Xiaoye S Li; Jennifer Loe; Piotr Luszczek; Srikara Pranesh; Siva Rajamanickam; Tobias Ribizel; Barry F Smith; Kasia Swirydowicz; Stephen Thomas; Stanimire Tomov; Yaohung M Tsai; Ulrike Meier Yang
• Keywords: ddc:510; 0101 mathematics; 01 natural sciences; Mathematics; info:eu-repo/classification/ddc/510; 510

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this work, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.