两类特殊矩阵方程的求解问题

兰州大学机构库 >数学与统计学院

	两类特殊矩阵方程的求解问题
Alternative Title	On the Solving of two particular Matrix Equation
	张秀英
Thesis Advisor	郑兵
	2010-05-29
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	最小范数解 R-对称奇异值分解克雷洛夫子空间全局的 Lanczos 算法交替分裂迭代方法 Sylvester矩阵方程
Abstract	本文分为两部分. 第一部分，我们研究的是复矩阵方程AXA^{H}=B的 Hermitian R-（反）对称解；利用奇异值分解，我们给出了其最小二乘解的表达式，进一步地，利用商奇异值分解，我们得到其极小范数最小二乘解.第二部分，我们考虑用克雷洛夫子空间方法求解具有特殊结构的大型Sylvester矩阵方程AX+XB=C. 基于HS分裂，我们给出的新算法可以解分裂得到的反对称部分. 首先用全局的Lanczos 算法生成克雷洛夫子空间的一组正交基，然后，由全局的满正交方(FOM), 得到新算法. 最后，通过具体的数值例子，我们将给出的算法与广义最小剩余法（GMRES）做了简单的比较.
Other Abstract	The paper include two parts.First,we consider the complex matrix equation AXA^{H}=B.Using SVDs,we give the formula of least squares solutions for Hermitian R-(skew) symmetric matrices,then we get the least norm solution by Q-SVD.In the second part,we describe Krylov subspace methods for solving large Sylvester equation AX+XB=C with some structure. The proposed algorithms use Krylov subspaces for which orthogonal bases are generated by the global Lanczos process.This makes the algorithms suitable for the matrix equation. Based on the symmetry and skew-symmetry splitting of the coefficient matrix,we get the new method from the FOM method. Numerical experiments and application are done to illustrate the effectiveness of the proposed algorithms compared with the GMRES method.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224882
Collection	数学与统计学院
Recommended Citation GB/T 7714	张秀英. 两类特殊矩阵方程的求解问题[D]. 兰州. 兰州大学,2010.

Files in This Item:
There are no files associated with this item.

If you have any objections to this item, please fill out the form below and the administrator will contact you as soon as possible.
Content:
Email：	*
Institution:
Verification Code:	Refresh

Any comments and suggestions are welcomed.
Title:	*
Content:
Email：	*
Verification Code:	Refresh

数学与统计学院知识库