秩亏矩阵极分解算法的扰动

The Perturbation of the Iterative Methods for Computing the Polar Decomposition of Rank-Deficient Matrix

针对[1]的算法,主要研究长方阵极分解迭代算法的扰动问题,考察误差对长方阵极分解迭代算法的影响,并给出扰动理论相关的数值例子.从试验结果可知,虽然极分解有着成熟的理论,但对于一般长方阵极分解的极分解算法,由于误差的不可避免性,并没有"绝对适用"的计算方法.

In this paper, our main focus is the perturbation of the method introduced in [1], which is used to solve polar decomposition. We study the error influence to rectangular matrix polar decomposition iteration arithmetic and also give some numberical examples. From numerical experiment, we draw a conclusion： there isn＇t ＂abslute credible＂ computing method to solve poloar decomposition.