兰州大学机构库 >数学与统计学院
求解病态Toeplitz系统的预处理研究
Alternative TitlePreconditioning research for solving ill conditioned Toeplitz systems
张佳霖
Thesis Advisor张国凤
2018-04-01
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword病态Toeplitz系统 预处理 迭代法 谱分布 收敛性
Abstract

Toeplitz系统具有丰富的应用背景, 其广泛地产生于科学计算, 信息论以及工程等众多的应用领域. 由于其通常表现出很强的病态性, 因此设计高效
预处理子改善相关算法的求解效率是有效求解这类问题的关键. 本文借鉴若干已知的有效预处理子的构造思路, 设计了一类既适用于病态对称的Toeplitz系统, 也适用于病态非对称的Toeplitz系统的新的预处理子. 此外, 利用Courant-Fischer极大极小定理分析了预处理矩阵的谱分布, 并且分析了相应Krylov子空间的收敛性质. 最后, 通过数值实验验证了所构造的处理子用来求解病态对称和非对称Toeplitz系统问题的可行性和有效性.

Other Abstract

Toeplitz systems have a rich background, which arise widely form many application areas, such as scientific computing, information theory and engineering. Due to its general ill-conditioning properties, it is critical to design efficient preconditioners to improve the efficiency of the related solution algorithms, so that we can solve these problems effectively. On the basis of the construction ideas of several efficient preconditioners, a class of new preconditioners are proposed, which are applicable for both the Hermitian and the non-Hermitian ill-conditioned Toeplitz systems. In addition, spectral distributions of the preconditioned matrices are analyzed based on
the Courant-Fischer minimax theorem, and the convergence properties of the corresponding Krylov space methods are studied. Finally, numerical experiments are presented to verify the feasibility and effectiveness of the constructed preconditioners for solving both the Hermitian and the non-Hermitian Toeplitz systems.

URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224806
Collection数学与统计学院
Recommended Citation
GB/T 7714
张佳霖. 求解病态Toeplitz系统的预处理研究[D]. 兰州. 兰州大学,2018.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[张佳霖]'s Articles
Baidu academic
Similar articles in Baidu academic
[张佳霖]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[张佳霖]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.