This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and $\mathtt{cr\_rsqrt}$, proposed for standardization in the C programming language as recommended by the IEEE-754 floating-point standard. The rounding to nearest (ties to even) and the non-stop arithmetic are assumed. The numerical examples compare the observed with theoretical bounds on the relative errors in the rotations' elements, and show that the maximal observed departure of the rotations' determinants from unity is smaller than that of the transformations computed by LAPACK.

翻译：本文展示了如何在温和假设下以高相对精度计算用于二阶厄米矩阵对角化的复雅可比旋转变换，利用IEEE-754浮点标准为C语言标准化推荐的正确舍入函数$\mathtt{cr\_hypot}$和$\mathtt{cr\_rsqrt}$。本文假设采用最近舍入（遇偶舍入）和无中断算术。数值实验将旋转变换元素相对误差的观测值与理论界限进行比较，结果表明旋转行列式与单位值的最大观测偏差小于通过LAPACK计算的变换所得偏差。