Representations and norm estimations for the Moore–Penrose inverse of multiplicative perturbations of matrices. Issue 3 (4th March 2017) - Zhang, Xiaobo; Fang, Xuxu; Song, Chuanning; Xu, Qingxiang
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.