scholarly journals Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

2007 ◽  
Vol 206 (2) ◽  
pp. 726-732 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Ting-Zhu Huang ◽  
Ying-Ding Fu
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Comparison 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.

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.

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

Comparison results for splitting iterations for solving multi-linear systems

2018 ◽  
Vol 134 ◽  
pp. 105-121 ◽  
Author(s):  
Wen Li ◽  
Dongdong Liu ◽  
Seak-Weng Vong
Keyword(s):  
Linear Systems ◽  
Comparison Results
Sign in / Sign up

Export Citation Format

Share Document