矩阵广义逆的乘法扰动界 Alternative Title On the Multiplicative Perturbation Bounds of Generalized Inverses 马培兰 Thesis Advisor 郑兵 2013-05-19 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 广义逆矩阵 g-逆 投影算子 {1,3}-逆 {1,4}-逆 {1,2,3}-逆 {1,2,4}-逆 2-范数 F-范数 Abstract 广义逆矩阵在求解线性方程组,优化问题,最小二乘问题中都有着广泛的应用.当矩阵的元素发生变化时,它的广义逆矩阵的元素也会发生相应的变化,对于所求解问题的结果也会产生相应的影响. 本文研究了矩阵广义逆的扰动界问题,得到了矩阵的广义逆在Frobenius 范数和谱范数下的加法扰动界和乘法扰动界.第三章给出了矩阵的g-逆和投影算子在Frobenius 范数和谱范数下的乘法扰动界; 第四章得到了矩阵的{1,3}-逆和{1,4}-逆在Frobenius 范数和谱范数下的加法扰动界和乘法扰动界; 第五章给出了矩阵的{1,2,3}-逆和{1,2,4}-逆在Frobenius 范数下的加法扰动界和乘法扰动界. Other Abstract 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 Chapter 3, we get the multiplicative perturbation bounds of the g-inverse and oblique projection under the spectral norm and Frobenius norm. In Chapter 4, we investigate 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 Chapter 5, we get the additive perturbation bounds and multiplicative perturbation bounds of the {1,2,3}-inverse and {1,2,4}-inverse under the Frobenius norm. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224992 Collection 数学与统计学院 Recommended CitationGB/T 7714 马培兰. 矩阵广义逆的乘法扰动界[D]. 兰州. 兰州大学,2013.
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