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.

混合精度数值线性代数算法的有效利用可以为科学计算应用提供诱人的加速。尤其是通过为机器学习应用程序设计的低精度特殊功能单元的硬件集成，传统的数字算法社区迫切需要重新考虑在不同操作中使用的浮点格式，以有效地利用可用的计算能力。在这项工作中，我们对混合精度数值线性代数例程进行了全面的调查，包括有关稠密和稀疏线性代数问题的基本概念，理论背景和实验结果。