Asynchronous Multisplitting GAOR Method and Asynchronous Multisplitting SSOR Method for Systems of Weakly Nonlinear Equations

被引：0
作者：
Mehdi Dehghan
Masoud Hajarian
机构：
[1] Amirkabir University of Technology,Department of Applied Mathematics, Faculty of Mathematics and Computer Science
来源：
Mediterranean Journal of Mathematics | 2010年 / 7卷
关键词：
Primary 65F10; Secondary 65H20; Multisplitting method; asynchronous; -matrix; -matrix; convergence; system of weakly nonlinear equations;
D O I：
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学科分类号：
摘要：
In this article, we introduce two new asynchronous multisplitting methods for solving the system of weakly nonlinear equations Ax = G(x) in which A is an n × n real matrix and G(x) = (g1(x), g2(x), . . . , gn(x))T is a P-bounded mapping. First, by generalized accelerated overrelaxation (GAOR) technique, we introduce the asynchronous parallel multisplitting GAOR method (including the synchronous parallel multisplitting AOR method as a special case) for solving the system of weakly nonlinear equations. Second, asynchronous parallel multisplitting method based on symmetric successive overrelaxation (SSOR) multisplitting is introduced, which is called asynchronous parallel multisplitting SSOR method. Then under suitable conditions, we establish the convergence of the two introduced methods. The given results contain synchronous multisplitting iterations as a special case.
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页码：209 / 223
页数：14
相关论文
共 55 条
[1]  
Arnal J.(1999)Non-stationary parallel multisplitting algorithms for almost linear systems Numer. Linear Algebra Appl. 6 79-92
[2]  
Migallón V.(1997)A class of two-stage iterative methods for systems of weakly nonlinear equations Numer. Algor. 14 295-319
[3]  
Penadés J.(1997)Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations Numer. Algor. 15 347-372
[4]  
Bai Z.Z.(1998)Asynchronous multisplitting two-stage iterations for systems of weakly nonlinear equations J. Comput. Appl. Math. 93 13-33
[5]  
Bai Z.Z.(1998)Asynchronous parallel nonlinear multisplitting relaxation methods for large sparse nonlinear complementarity problems Appl. Math. Comput. 92 85-100
[6]  
Bai Z.Z.(1998)The convergence of the two-stage iterative method for hermitian positive definite linear systems Appl. Math. Lett. 11 1-5
[7]  
Huang Y.G.(1999)Asynchronous multisplitting AOR methods for a class of systems of weakly nonlinear equations Appl. Math. Comput. 98 49-59
[8]  
Bai Z.Z.(2003)Convergence theorems for parallel multisplitting twostage iterative methods for mildly nonlinear systems Linear Algebra Appl. 362 237-250
[9]  
Bai Z.Z.(1995)Parallel synchronous and asychronous two-stage multisplitting methods Electronic Transactions on Numerical Analysis 3 24-38
[10]  
Bai Z.Z.(1998)Models of parallel chaotic iteration methods Linear Algebra Appl. 103 175-192
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