scholarly journals Iterative methods for solving absolute value equations

2021 ◽  
Vol 26 (04) ◽  
pp. 322-329
Author(s):  
R. Ali ◽  
A. Ali ◽  
S. Iqbal
Keyword(s):  
Iterative Methods ◽  
Absolute Value Equations ◽  
Absolute Value

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.

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.

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

scholarly journals Modified SOR-Like Method for Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Fixed Point ◽  
Nonlinear Equation ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Absolute Value Equations ◽  
Convergence Conditions ◽  
Absolute Value ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Better Than

In this paper, based on the work of Ke and Ma, a modified SOR-like method is presented to solve the absolute value equations (AVE), which is gained by equivalently expressing the implicit fixed-point equation form of the AVE as a two-by-two block nonlinear equation. Under certain conditions, the convergence conditions for the modified SOR-like method are presented. The computational efficiency of the modified SOR-like method is better than that of the SOR-like method by some numerical experiments.

A new SOR-like method for solving absolute value equations

2020 ◽  
Vol 156 ◽  
pp. 410-421
Author(s):  
Xu Dong ◽  
Xin-Hui Shao ◽  
Hai-Long Shen
Keyword(s):  
Absolute Value Equations ◽  
Absolute Value

Brief Reports: The Interaction of Spatial Visualization and General Reasoning Abilities with Instructional Treatment on Absolute Value Equations

1978 ◽  
Vol 9 (2) ◽  
pp. 152-154
Author(s):  
Phillip M. Eastman ◽  
Mohammed Salhab
Keyword(s):  
Individual Differences ◽  
Spatial Visualization ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Reasoning Abilities ◽  
Instructional Treatment ◽  
Treatment Interaction ◽  
Aptitude Treatment Interaction ◽  
Method Of Instruction

Aptitude treatment interaction (ATI) studies essentially deal with two related questions: Can we adapt instruction to patterns of individual differences among students? If so, for which students is a particular method of instruction most effective? The general ATI problem as advanced by Cronbach (1957) is well known (e.g., Becker, 1970), and no further discussion of it is presented here.

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