Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This paper shows an algorithm that reduces the number of operations to compute the entries of a Givens rotation. Overall, the new algorithm has more operations in total when compared to algorithms in different releases of LAPACK, but less operations per entry. Numerical tests show that the new algorithm is more accurate on average.

翻译：在浮精度计算中生成 2x-2 单元矩阵是一个微妙的任务。 减少累积错误的方法之一是使用低浮点操作来计算2x2单数矩阵中的每个条目。 本文显示了一种减少操作数量的算法, 以计算 Gives 旋转的条目。 总体而言, 新算法的总操作比LAPACK 不同版本的算法要多, 但每条目的算法要少。 数字测试显示新算法平均更准确 。