Today’s floating-point arithmetic landscape is broader than ever. While scientific computing as traditionally used single precision and double precision floating-point arithmetics, half precision is increasingly available in hardware and quadruple precision is supported in software. Lower precision arithmetic brings increased speed and reduced communication and energy costs, but it produces results of correspondingly low accuracy. Higher precisions are more expensive but can potentially provide great benefits, even if used sparingly.

A variety of mixed precision numerical linear algebra algorithms have been developed that combine the superior performance of lower precisions with the better accuracy of higher precisions. We identify key algorithmic ideas, such as iterative refinement by Newton’s method, adapting the precision to the data, and multiword arithmetic, and illustrate them through recent research. The ideas we describe can be useful to a wide community of researchers and practitioners who wish to develop or benefit from mixed precision numerical linear algebra algorithms.

Zoom Link:  https://argonne.zoomgov.com/j/1617875658

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