Mixed precision algorithms in numerical linear algebra
نویسندگان
چکیده
Today’s floating-point arithmetic landscape is broader than ever. While scientific computing has traditionally used single precision and double arithmetics, half increasingly available in hardware quadruple supported software. Lower brings increased speed reduced communication energy costs, but it produces results of correspondingly low accuracy. Higher precisions are more expensive can potentially provide great benefits, even if sparingly. A variety mixed algorithms have been developed that combine the superior performance lower with better accuracy higher precisions. Some these aim to same quality as running a fixed at much cost; others use little improve an algorithm. This survey treats broad range numerical linear algebra, both direct iterative, for problems including matrix multiplication, factorization, systems, least squares, eigenvalue decomposition singular value decomposition. We identify key algorithmic ideas, such iterative refinement, adapting data, exploiting block fused multiply–add operations. also describe possible benefits explain what known about stability algorithms. should be useful wide community researchers practitioners who wish develop or benefit from algebra
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ژورنال
عنوان ژورنال: Acta Numerica
سال: 2022
ISSN: ['0962-4929', '1474-0508']
DOI: https://doi.org/10.1017/s0962492922000022