吉文斯旋转的数值分析
Numerical analysis of Givens rotation
摘要：
在浮点数运算中，生成2乘2的酉矩阵是一项精细的任务。减少累积误差的一种方法是使用较少的浮点运算来计算2 × 2酉矩阵中的每个条目。本文提出了一种算法，减少了操作的数量来计算一个吉文斯旋转的条目。总的来说，新算法与LAPACK的不同版本中的算法相比，总共具有更多的操作，但每个条目的操作较少。数值试验表明，新算法的平均精度更高。
英文摘要：
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.
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