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Preconditioned iterative method and parallel alternating two iterative methods of analysis

Author: ZhangNing
Tutor: WangGuangBin
School: Qingdao University of Science and Technology
Course: Applied Mathematics
Keywords: Pre- conditions AOR iterative method Mixed-type splitting iterative method Alternating two parallel iterative method Convergence Theorem Comparison theorem
CLC: O241.6
Type: Master's thesis
Year: 2010
Downloads: 44
Quote: 0
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Abstract


Stationary iterative method for solving large linear equations of a class of very important ways . However, with the rapid development of science and technology needs to solve the problem of the increasing scale , for the steady -based matrix splitting iteration method , when the spectral distribution is very scattered , the general convergence speed is very slow, or even not converge . So the linear equations using the coefficient matrix spectral pretreatment technology gathered to solve the problem of the convergence of the effective ways to become a hot research iteration problem . This paper studies based on specific matrix preconditioned iterative algorithms and parallel alternating two iterative algorithm gives several new pre- conditions for the child , the case study of a new preconditioned iterative method and comparison theorem, improved Some recent results, and gives several new algorithms . This paper is divided into five chapters , the main focus is reflected in the third innovation ﹑ fourth and fifth chapters . The first chapter is the introduction , the main topic of this paper outlines the background and main tasks. The second chapter is preliminary knowledge , introduces the basic knowledge related to this article . The third chapter is the coefficient matrix of linear equations for the Z- matrix, the coefficient matrix with several types of preconditioners treatment, and then the classic AOR iterative method for solving research . Main iterative method is given after pretreatment convergence , Preconditioned iterative matrix iterative matrix convergence speed and convergence rate of the original comparison , and gives the child in the pre- conditions for the convergence rate is not the same comparison . The fourth chapter is the coefficient matrix of linear equations for the Z- matrix, the coefficient matrix with several types of preconditioners treatment, reuse Mixed-type splitting iterative method for solving research, given a number of research results. The fifth chapter is the coefficient matrix of the linear equations for the monotone matrix , H- matrix, established parallel multi- split two alternating iterative methods , and discusses the convergence of the method , and thus gives two relaxation type iteration method and its convergence theorem .

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