Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem

1984 ◽  
Vol 42 (1) ◽  
pp. 1-17 ◽  
Author(s):  
J. S. Pang
Keyword(s):  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Linear Complementarity ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

scholarly journals High-Order Iterative Methods for the DMP Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoji Liu ◽  
Naping Cai
Keyword(s):  
Error Estimate ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
High Order Iterative Methods

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

scholarly journals A convergence analysis of SOR iterative methods for linear systems with weak H-matrices

2016 ◽  
Vol 14 (1) ◽  
pp. 747-760
Author(s):  
Cheng-yi Zhang ◽  
Zichen Xue ◽  
Shuanghua Luo
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Convergence Results ◽  
Diagonally Dominant Matrices ◽  
Diagonally Dominant ◽  
Necessary And Sufficient

AbstractIt is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.

scholarly journals A Preconditioned Multisplitting and Schwarz Method for Linear Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cuiyu Liu ◽  
Chen-liang Li
Keyword(s):  
Convergence Rate ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Coefficient Matrix ◽  
Schwarz Method

The preconditioner presented by Hadjidimos et al. (2003) can improve on the convergence rate of the classical iterative methods to solve linear systems. In this paper, we extend this preconditioner to solve linear complementarity problems whose coefficient matrix isM-matrix orH-matrix and present a multisplitting and Schwarz method. The convergence theorems are given. The numerical experiments show that the methods are efficient.

scholarly journals Relaxed Modulus-Based Matrix Splitting Methods for the Linear Complementarity Problem

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 503
Author(s):  
Shiliang Wu ◽  
Cuixia Li ◽  
Praveen Agarwal
Keyword(s):  
Fixed Point ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Linear Complementarity ◽  
Splitting Methods ◽  
Matrix Splitting ◽  
Numerical Examples ◽  
Iteration Methods ◽  
Point Form

In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity problem. Some sufficient conditions for guaranteeing the convergence of relaxed modulus-based matrix splitting iteration methods are presented. Numerical examples are offered to show the efficacy of the proposed methods.

A Preconditioned Gauss-Seidel Iterative Method for Linear Complementarity Problem in Intelligent Materials System

2011 ◽  
Vol 340 ◽  
pp. 3-8 ◽  
Author(s):  
Ban Xiang Duan ◽  
Wen Ying Zeng ◽  
Xiao Ping Zhu
Keyword(s):  
Iterative Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Linear Complementarity ◽  
Computational Results ◽  
System Matrix ◽  
Intelligent Materials ◽  
Preconditioned Matrix ◽  
Set Up

In this paper, the authors first set up new preconditioned Gauss-Seidel iterative method for solving the linear complementarity problem, whose preconditioned matrix is introduced. Then certain elementary operations row are performed on system matrix before applying the Gauss-Seidel iterative method. Moreover the sufficient conditions for guaranteeing the convergence of the new preconditioned Gauss-Seidel iterative method are presented. Lastly we report some computational results with the proposed method.

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