α-β广义逆的扰动理论及其应用  

Perturbation Theory for the α-β Generalized Inverse with Application

作　　者：蔡静[1] 朱超[1] 陈果良[1] 

机构地区：[1]华东师范大学数学系,上海200062

出　　处：《华东师范大学学报（自然科学版）》2001年第4期22-27,共6页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金 (1 9871 0 2 9)

摘　　要：该文讨论了α β广义逆的扰动理论。在B =A +E∈Cm×n,R(E) R(A) ,R(E ) R(A )及Δ =‖A(- 1 )αβ E‖ ββ<1(其中α ,β是本性严格凸范数 )的条件下 ,给出了B(- 1 )αβ -A(- 1 )αβ 的分解式 ,进而有α β广义逆扰动的范数估计。作为一个应用 ,还讨论了线性方程组Ax =b的唯一的极小In this paper, a perturbation theory for the α β generalized inverse A (-1) αβ is developed. Let B=A+E∈C m×n , R(E)R(A), R(E *)R(A *) and Δ=‖A (-1) αβ E‖ ββ <1 , where α,β are e.s.c norms on C m, C n , respectively. Then we put forward a useful decomposition of B (-1) αβ -A (-1) αβ . As a result, norm estimate of ‖B (-1) αβ -A (-1) αβ ‖ βα is presented. We also get a perturbation bound of the unique minimal β norm α approximate solution of the system Ax=b .

关 键 词：a-β广义逆 扰动理论 严格凸 范数估计 

分 类 号：O151.21[理学—数学]