| 群逆的扰动界及其在奇异线性系统中的应用 |
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| 引用本文： | 魏益民.群逆的扰动界及其在奇异线性系统中的应用[J].数学年刊A辑(中文版),2003(1). |
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| 作者姓名： | 魏益民 |
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| 作者单位： | 复旦大学数学系和非线性数学教育部重点实验室 上海 |
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| 基金项目： | 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 |
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| 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.
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| 关 键 词： | 群逆 Jordan标准形 扰动界 奇异线性系统 |
ON THE PERTURBATION BOUND OF THE GROUP INVERSE WITH APPLICATION TO SINGULAR LINEAR SYSTEM |
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| WEI Yimin.ON THE PERTURBATION BOUND OF THE GROUP INVERSE WITH APPLICATION TO SINGULAR LINEAR SYSTEM[J].Chinese Annals of Mathematics,2003(1). |
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| Authors: | WEI Yimin |
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| Affiliation: | WEI YiminDepartment of Mathematics and Laboratory of Mathematics for Nonlinear Science,Fudan University,Shanghai 200433,China. E-mail: ymwei@fudan.edu.cn |
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| Abstract: | 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. |
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| Keywords: | Group inverse Jordan canonical form Perturbation bound Singular linear system |
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