A New Iterative Method for Solving Absolute Value Equations

2016 ◽  
Author(s):  
Jing Li ◽  
Fei Qin ◽  
Jie Liu ◽  
Bin Zhou
Keyword(s):  
Iterative Method ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
New Iterative Method

scholarly journals Iterative schemes induced by block splittings for solving absolute value equations

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4171-4188
Author(s):  
Nafiseh Shams ◽  
Alireza Fakharzadeh Jahromi ◽  
Fatemeh Beik
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Numerical Experiments ◽  
Sufficient Conditions ◽  
Convergence Properties ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Iterative Schemes ◽  
Generalized Newton ◽  
Special Case

In this paper, we develop the idea of constructing iterative methods based on block splittings (BBS) to solve absolute value equations. The class of BBS methods incorporates the well-known Picard iterative method as a special case. Convergence properties of mentioned schemes are proved under some sufficient conditions. Numerical experiments are examined to compare the performance of the iterative schemes of BBS-type with some of existing approaches in the literature such as generalized Newton and Picard(-HSS) iterative methods.

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 An optimized AOR iterative method for solving absolute value equations

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 459-476
Author(s):  
Alireza Fakharzadeh Jahromi ◽  
Nafiseh Shamsa
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Optimization Techniques ◽  
Optimal Parameters ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Sor Methods ◽  
Two Parameters

In recent years, the AOR iterative method has been proposed for solving absolute value equations. This method has two parameters ? and ?. In this paper, we intend to find the optimal parameters of this method to improve convergence rate by suitable optimization techniques. Meanwhile, the convergence of the optimized AOR iterative method is discussed. It is both theoretically and experimentally demonstrated efficiency of the optimized AOR iterative method in contrast with the AOR and SOR methods.

scholarly journals Residual Iterative Method for Solving Absolute Value Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Javed Iqbal ◽  
Eisa Al-Said
Keyword(s):  
Iterative Method ◽  
Method Comparison ◽  
Absolute Value Equations ◽  
Projection Technique ◽  
Absolute Value

We suggest and analyze a residual iterative method for solving absolute value equationsAx-x=bwhereA∈Rn×n,b∈Rnare given andx∈Rnis unknown, using the projection technique. We also discuss the convergence of the proposed method. Several examples are given to illustrate the implementation and efficiency of the method. Comparison with other methods is also given. Results proved in this paper may stimulate further research in this fascinating field.

On an iterative method for solving absolute value equations

2011 ◽  
Vol 6 (5) ◽  
pp. 1027-1033 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Javed Iqbal ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said
Keyword(s):  
Iterative Method ◽  
Absolute Value Equations ◽  
Absolute Value

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

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