scholarly journals Convergence Analysis of Preconditioned AOR Iterative Method for Linear Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Qingbing Liu ◽  
Guoliang Chen
Keyword(s):  
Iterative Method ◽  
Rate Of Convergence ◽  
Linear Systems ◽  
Optimization Theory ◽  
Convergence Result ◽  
Comparison Theorems ◽  
Car Industry ◽  
Fluid Analysis ◽  
Comparison Results ◽  
Preconditioned Iterative

M-(H-)matrices appear in many areas of science and engineering, for example, in the solution of the linear complementarity problem (LCP) in optimization theory and in the solution of large systems for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to convergence for this class of matrices. In this paper, we present some comparison theorems on the preconditioned AOR iterative method for solving the linear system. Comparison results show that the rate of convergence of the preconditioned iterative method is faster than the rate of convergence of the classical iterative method. Meanwhile, we apply the preconditioner toH-matrices and obtain the convergence result. Numerical examples are given to illustrate our results.

scholarly journals A modified AOR-type iterative method for L-matrix linear systems

2007 ◽  
Vol 49 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Shiliang Wu ◽  
Tingzhu Huang
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Rates ◽  
Comparison Theorems ◽  
Iterative Schemes ◽  
Seidel Method ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

AbstractBoth Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.

Convergence Analysis of Preconditioned SSOR Iterative Method for Linear Systems

2014 ◽  
Vol 644-650 ◽  
pp. 1988-1991
Author(s):  
Ting Zhou
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Result ◽  
Numerical Example ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. In this paper, we present preconditioned SSOR iterative method for solving the linear systems. Meanwhile, we apply the preconditioner to H-matrix and obtain the convergence result. Finally, a numerical example is also given to illustrate our results.

A Preconditioned AOR Iterative Method for the Absolute Value Equations

2017 ◽  
Vol 14 (02) ◽  
pp. 1750016 ◽  
Author(s):  
Cui-Xia Li
Keyword(s):  
Iterative Method ◽  
Comparison Theorems ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Comparison Results ◽  
Preconditioning Technique ◽  
The Matrix ◽  
The Absolute ◽  
Theoretical Results ◽  
Better Than

In this paper, coupled with preconditioning technique, a preconditioned accelerated over relaxation (PAOR) iterative method for solving the absolute value equations (AVEs) is presented. Some comparison theorems are given when the matrix of the linear term is an irreducible [Formula: see text]-matrix. Comparison results show that the convergence rate of the PAOR iterative method is better than that of the accelerated over relaxation (AOR) iterative method whenever both are convergent. Numerical experiments are provided in order to confirm the theoretical results studied in this paper.

scholarly journals Some Results on Preconditioned Mixed-Type Splitting Iterative Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Guangbin Wang ◽  
Fuping Tan
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Mixed Type ◽  
Comparison Theorems ◽  
Numerical Example

We present a preconditioned mixed-type splitting iterative method for solving the linear system Ax=b, where A is a Z-matrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give one numerical example to illustrate our results.

Comparison Results on Preconditioned AOR-Type Iterative Method for M-Matrices

2013 ◽  
Vol 756-759 ◽  
pp. 2629-2633
Author(s):  
Ting Zhou ◽  
Hong Fang Cui
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Iterative Method ◽  
Iterative Methods ◽  
Science And Engineering ◽  
Numerical Example ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. M-matrices appear in many areas of science and engineering. In this paper, we present preconditioned AOR-type iterative method and the SOR-type iterative method with a preconditioner for solving the M-matrices. In addition, the relation between the convergence rate of preconditioned AOR-type iterative method and the parameters are brought to light. Finally, a numerical example is also given to illustrate the results.

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