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Pre-conditions For Solution Of Linear Systems

Posted on:2009-12-12Degree:MasterType:Thesis
Country:ChinaCandidate:H Y ZhaoFull Text:PDF
GTID:2190360242993294Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
The thesis mainly deals with how to accelerate the rate of convergence for the large-scale linear equations. As is well known, many problems are reduced to one or more of large (usually sparse) linear equations as a matter of fact. The iterative method is the usual way to solve the equations ,its convergence and its rate of convergence are great significa- nce , an iterative method doesn't work, while that has a low rate of convergence is no practical value. An iterative format that has a better rate of convergence must be found, the parameters in the format be determined, and the autologous improvements on the iterative format, and one of these ways is to seek better iterative method which has a fast rate of convergence. Concretely, the preconditioner Pα= I+Cαis applied to SOR iterative method( MSOR iterative method).This text includes five chapters. Chapter one is the introduction of the paper, mainly to discuss some common iterative methods and to introduce preconditioned theory and cited the preconditioned matrix Pα= I+Cαto propose by Hadjidmos. In chapter two , the writer provides the basic knowledge and the basic lemma required in this paper. The third chapter is an outline of the conclusions about preconditioner for the development of the theory in recent years . From the beginning of chapter four is the essence of the thesis and here we give details for chapter four and five .In the fourth chapter, the author discusses the convergence of the modified SOR ite- rative method which the preconditioner Pαis applied to SOR iterative method, when the matrix A is strictly diagonally dominant L -matrix or H -matrix. And a brief description of the parameters αfor the best selection from the preconditioner Pα= I+Cα. At last, numerical examples are also given, which show the effectiveness of our method.Chapter five, we discuss the preconditioner Pα= I+Cαwhich accelerates the rate of convergence for iterative method. First, the author discusses the convergence of the modified SOR iterative method to accelerate SOR iterative method, when the matrix A is the nonsingular M - matrix, and gives the best parametersωof the MSOR iterative method and then we discuss that the rate of convergence of MSOR iterative method is faster than the AOR iterative method where reflects the advantage of the practical value of Pαand then we change a way to structure a series of preconditioner Pαi that proves the same method to enhance the convergence rate of SOR iterative method, but the convergence rate of the method which the preconditioners Pαi are applied to SOR iterative method ( ISOR iterative method) is lower thanMSOR and then numerical examples are also given, which show the effectiveness of our method.Finally, the author describes the material train of thought and research foreground of his article.
Keywords/Search Tags:preconditioned method, nonsingularM-matrix, SORiterative method, convergence, comparison theorem
PDF Full Text Request
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