一种计算 Givens 旋转的快速补偿算法
A Fast Compensated Algorithm for Computing Givens Rotations
AI总结：
本文提出一种简单补偿方案计算高精度 Givens 旋转，该算法利用初步计算结果构建自身修正，且在斜边计算精度较低时仍保持高精度。
摘要：
我们开发了一种非常简单的补偿方案，用于计算非常精确的 Givens 旋转。该方法比 \cite{borges2021fast} 中的方法明显更直接，其推导导出了一个令人非常满意的算法，即一个简单计算得到的 Givens 旋转可用于构建对其自身的修正。此外，可以看到，即使该方案建立在精度较低的斜边计算之上，它仍能继续提供高精度。
英文摘要：
We develop a very simple compensated scheme for computing very accurate Givens rotations. The approach is significantly more straightforward than the one in \cite{borges2021fast}, and the derivation leads to a very satisfying algorithm whereby a naively computed Givens rotation can be used to construct a correction to itself. It is also seen that this scheme continues to provide high accuracy even when built on a hypoteneuse calculation that is of lesser accuracy.
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。
