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：本说明展示了如何在温和假设下，利用C语言中依据IEEE-754浮点标准推荐标准化而提出的正确舍入函数 $\mathtt{cr\_hypot}$ 和 $\mathtt{cr\_rsqrt}$，以高相对精度计算用于二阶厄米矩阵对角化的复Jacobi旋转。假设采用最近舍入（遇偶取整）及无中断算术模式。数值实验将旋转元素相对误差的观测值与理论界进行比较，结果表明旋转行列式偏离单位矩阵的最大观测值小于LAPACK计算所得变换的对应值。