混合精度矩阵计算中的误差平衡
Balancing Inexactness in Mixed Precision Matrix Computations
AI总结：
本文探讨了在存在其他不精确性来源时，如何通过混合精度计算平衡误差以提高性能。
摘要：
在新兴的高性能架构中，支持多种精度和数制的算术正变得越来越普遍。从计算科学家的角度来看，我们的目标是确定如何以及在哪里可以安全地利用混合精度计算来提高性能。在存在其他显著的"不精确性"来源的情况下，例如离散化误差、测量误差或算法近似误差时，使用低精度是自然且常见的。在这些情况下，分析这些不同来源的不精确性可以提供关于如何选择各种计算的精度以"平衡"误差的见解，从而可能在不明显降低准确性的情况下提高性能。我们展示了几个最近的例子，证明了在数值线性代数和矩阵计算中使用混合精度的潜力。
英文摘要：
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely exploit mixed precision computation in our codes to improve performance. One case where the use of low precision is natural, common in computational science, is when there are already other significant sources of ``inexactness'' present, e.g., discretization error, measurement error, or algorithmic approximation error. In such instances, analyzing the interaction of these different sources of inexactness can give insight into how the precisions of various computations should be chosen in order to ``balance'' the errors, potentially improving performance without a noticeable decrease in accuracy. We present a few recent examples of this approach which demonstrate the potential for the use of mixed precision in numerical linear algebra and matrix computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
