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：本说明展示了如何利用C语言中按照IEEE-754浮点标准推荐标准化使用的正确舍入函数$\mathtt{cr\_hypot}$和$\mathtt{cr\_rsqrt}$，在温和假设下以高相对精度计算用于对角化二阶厄米矩阵的复雅可比旋转。假定采用就近舍入（平局舍入至偶数）及无中断算术。数值实验将旋转矩阵元素相对误差的观测值与理论界进行了比较，结果表明旋转矩阵行列式偏离单位量的最大观测值小于LAPACK计算变换的相应值。