The solution of the absolute value equations using two generalized accelerated overrelaxation methods

2021 ◽  
Author(s):  
Rashid Ali ◽  
Kejia Pan
Keyword(s):  
Numerical Results ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
The Absolute

Finding the solution of the absolute value equations (AVEs) has attracted much attention in recent years. In this paper, we propose and analyze two generalized accelerated overrelaxation (AOR) methods for solving AVEs [Formula: see text], where [Formula: see text] is an [Formula: see text]-matrix. Furthermore, we discuss the convergence of the methods under some suitable assumptions. Numerical results are given to verify the effectiveness of our methods.

scholarly journals The Picard-HSS-SOR iteration method for absolute value equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lin Zheng
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equation ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Convergence Results ◽  
Hss Iteration ◽  
The Absolute ◽  
Hss Iteration Method

AbstractIn this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

A Smoothing Newton Method for Solving Absolute Value Equations

2013 ◽  
Vol 765-767 ◽  
pp. 703-708 ◽  
Author(s):  
Xiao Qin Jiang
Keyword(s):  
Newton Method ◽  
Numerical Results ◽  
Smoothing Newton Method ◽  
Absolute Value Equations ◽  
Absolute Value

In this paper, we reformulate the system of absolute value equations as afamily of parameterized smooth equations and propose a smoothing Newton method tosolve this class of problems. we prove that the method is globally and locally quadraticallyconvergent under suitable assumptions. The preliminary numerical results demonstratethat the method is effective.

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 Merit functions for absolute value variational inequalities

2021 ◽  
Vol 6 (11) ◽  
pp. 12133-12147
Author(s):  
Safeera Batool ◽  
◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Keyword(s):  
Variational Inequalities ◽  
Error Bounds ◽  
Complementarity Problem ◽  
Merit Functions ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Special Cases ◽  
The Absolute

<abstract><p>This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.</p></abstract>

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