On The Multiplicative Perturbation Bounds Of Generalized Inverses

Generalized inverse plays an important role in widely fields, such as the solution of linear system, optimization theory and methods and the least square problem. When the elements of a matrix change, the same thing happens to its generalized inverse, so the solution of the problem changes as well.In this page, we study the perturbation bounds of the generalized inverse, and get the additive perturbation bounds and multiplicative perturbation bounds of some generalized inverses under the Frobenius norm and spectral norm. In Chapter3, we get the multiplicative perturbation bounds of the g-inverse and projector under the spectral norm and Frobenius norm. In Chapter4, we inves-tigate the additive perturbation bounds and multiplicative perturbations bounds of the{1,3}-inverse and{1,4}-inverse under the Frobenius norm and spectral norm. And in Chapter5, we get the additive perturbation bounds and multi-plicative perturbation bounds of the{1.2,3}-inverse and{1,2,4}-inverse under the Frobenius norm.