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 Subtype 硕士 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 CitationGB/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.
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