Representations and norm estimations for the Moore–Penrose inverse of multiplicative perturbations of matrices. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Zhang, Xiaobo; Fang, Xuxu; Song, Chuanning; Xu, Qingxiang
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 3(2017)
• Page Start: 555
• Page End: 571
• Publication Date: 2017-03-04
• Subjects: Moore–Penrose inverse -- multiplicative perturbation -- norm upper bound; 15A09; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1197175
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : A multiplicative perturbation of a matrix has the form with and, which can be expressed alternatively as, where is the Moore–Penrose inverse of T, and are introduced as In view of the above and, a new type of multiplicative perturbation called weak perturbation is introduced. A formula for is derived in the general case that is a weak perturbation of T . Based on this formula, an upper bound for is derived. The sharpness of the obtained upper bound is illustrated by some numerical examples.