Representations and norm estimations for the Moore-Penrose inverse of multiplicative perturbations of matrices

作者：Zhang, Xiaobo; Fang, Xuxu; Song, Chuanning; Xu, Qingxiang^*

来源：Linear and Multilinear Algebra, 2017, 65(3): 555-571.

DOI：10.1080/03081087.2016.1197175

• Moore-Penrose inverse
• multiplicative perturbation
• norm upper bound

A multiplicative perturbation of a matrix T is an element of C-mxn has the form ETF* with E is an element of C-mxm and F is an element of C-nxn, which can be expressed alternatively as LET(R-F)*, where T+ is the Moore-Penrose inverse of T, L-E and R-F are introduced as
L-E = ETT+ + I-m -TT+, R-F = T+ T-F + I-n -T+ T.
In view of the above L-E and R-F, a new type of multiplicative perturbation called weak perturbation is introduced. A formula for (ETF*)+ is derived in the general case that ETF* is a weak perturbation of T. Based on this formula, an upper bound for parallel to(ETF*)(+) -T+parallel to 2 is derived. The sharpness of the obtained upper bound is illustrated by some numerical examples.

• 出版日期2017
• 单位上海师范大学