广义极分解与加权极分解的扰动界

兰州大学机构库 >数学与统计学院

	广义极分解与加权极分解的扰动界
Alternative Title	The perturbation bounds for generalized polar decomposition and weighted polar decomposition
	洪肖丽
Thesis Advisor	郑兵
	2014-05-29
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	广义极分解半正定极因子次酉极因子加权极分解广义非负极因子加权酉极因子
Abstract	矩阵的广义极分解和加权极分解在许多领域都扮演着非常重要的角色, 如数值分析, 矩阵逼近, 尤其是矩阵理论的研究等方面. 然而, 对于广义极分解和加权极分解的扰动问题, 许多的学者已经作了大量的研究工作并且给出了一些很好的扰动界.在此基础上, 我们进一步的研究这一问题. 本文主要是在保秩情况下研究广义极分解和加权极分解的扰动的, 首先, 分别给出了(广义)极分解的(半)正定极因子和(次)酉极因子在酉不变范数和谱范数下的新的加法扰动界; 其次, 根据广义极分解和加权极分解之间的关系, 不加证明的给出了加权极分解的加法扰动界并改进了已有的结果. 最后, 对加权极分解的乘法扰动做了具体的研究, 给出广义非负极因子和加权酉极因子在不同加权范数下的新的扰动界并提高了已有的结果.
Other Abstract	The generalized polar decomposition and weighted polar decomposition play an important role in many fields of numerical analysis, matrix approximation and so on, especially on the matrix theory research. Moreover, many researchers have already studied and presented a lot of classical perturbation results of the perturbation problems for generalized polar decomposition and weighted polar ecomposition. Based on this, we further study the problem. In this paper, we study the perturbation of the generalized polar decomposition and weighted polar decomposition under the same rank. Firstly, some new perturbation bounds of positive (semi)definite polar factor and (sub)unitary polar factor for (generalized) polar decomposition under the general unitarily invariant norm and the spectral norm are presented; Secondly, according to the connection between generalized polar decomposition and weighted polar decomposition, we directly give out the perturbation bounds for weighted polar decomposition without proof which improve the known results. Finally, we further consider the multiplicative perturbation of the weighted polar decomposition, and present some new perturbation bounds for the generalized nonnegative and weighted unitary polar factors under the different weighted norms which improve the existing perturbation bounds.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225312
Collection	数学与统计学院
Recommended Citation GB/T 7714	洪肖丽. 广义极分解与加权极分解的扰动界[D]. 兰州. 兰州大学,2014.

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