论文标题
Givens旋转的数值分析
Numerical analysis of Givens rotation
论文作者
论文摘要
在浮动精确算术中生成2 by-2统一的矩阵是一项微妙的任务。减少累积错误的一种方法是使用较少的浮点操作来计算2 by-2统一矩阵中的每个条目。本文显示了一种算法，该算法减少了计算Givens旋转条目的操作数量。总体而言，与Lapack不同发行版中的算法相比，新算法总共具有更多的操作，但每个条目的操作更少。数值测试表明，新算法平均更准确。
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.
