次酉极因子在酉不变范数下的相对扰动界

Relative Perturbation Bounds for the Subunitary Polar Factor Under Unitarily Invariant Norms

设A是一个m×n阶复矩阵,分解A=QH称为广义极分解,如果Q是m×n次酉极因子且H为n×n半正定的Hermite矩阵．本文获得了次酉极因子在任意酉不变范数下的几个相对扰动界,在某种意义上,相对扰动界比R．C．Li等获得的绝对扰动界要好．

Let A be an m x n complex matrix, A decomposition A = QH is said to be a generalized polar decomposition of A if Q is an m ×n subunitary matrix and H is an n ×n Hermitian positive semidefinite matrix. In this paper, some relative perturbation bounds of the subunitary polar factor under unitarily invariant norms are presented, which are tighter in some sense, compared with the absolute perturbation bounds obtained by Li C. R. and so on.