群逆的扰动界及其在奇异线性系统中的应用  

ON THE PERTURBATION BOUND OF THE GROUP INVERSE WITH APPLICATION TO SINGULAR LINEAR SYSTEM

作　　者：魏益民[1] 

机构地区：[1]复旦大学数学系和非线性数学教育部重点实验室,上海200433

出　　处：《数学年刊（A辑）》2003年第1期23-32,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19901006);国家教育部博士点基金;中国留学基金委资助的项目

摘　　要：本文建立了群逆的扰动界,此界基于矩阵A的Jordan标准形和P-范数,其中P是非异矩阵满足 是非异上双对角阵且 当矩阵A和A+E有相同的秩且 较小时,得到了 较好的估计.在相同的条件下,研究了相容的奇异线性系统Aχ=b的扰动,给出了χopt=A#b扰动的上界,其中A#是A的群逆,χopt是最小P-范数解.A perturbation bound for the group inverse is developed. This bound is based on the Jordan canonical form and P-norm of A, where P is an invertible matrix such that and D is a nonsingular upper bidiagonal matrix withSharp estimates of p are derived when A and A + E are of the same rank and p is small. Under similar conditions the perturbation of a singular consistent linear system Ax = b is studied. Realistic bounds on the perturbation of xopi = A#b is presented, where xopt is the minimal P-norm solution.

关 键 词：群逆 JORDAN标准形 扰动界 奇异线性系统 

分 类 号：O151.21[理学—数学] O241.1[理学—基础数学]