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.

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.

scholarly journals Analysis of Patch Substructuring Methods

2007 ◽  
Vol 17 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Martin Gander ◽  
Laurence Halpern ◽  
Frédéric Magoulès ◽  
François-Xavier Roux
Keyword(s):  
Convergence Rate ◽  
Numerical Experiments ◽  
Decomposition Methods ◽  
Transmission Conditions ◽  
New Method ◽  
Domain Decomposition Methods ◽  
Convergence Properties ◽  
Schwarz Method ◽  
Overlapping Domain Decomposition ◽  
Special Case

Analysis of Patch Substructuring MethodsPatch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.

scholarly journals Group Splitting with SOR/AOR Methods for Solving Boundary Value Problems: A Computational Comparison

2021 ◽  
Vol 14 (3) ◽  
pp. 905-914
Author(s):  
Abdulkafi Mohammed Saeed ◽  
Najah Mohammad AL-harbi
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Iterative Methods ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Elliptic Partial Differential Equations ◽  
The Other ◽  
Alternative Methods ◽  
Group Methods ◽  
Computational Comparison

Many researchers are working on the explicit group methods as the alternative methods for solving several boundary value problems. These methods have been shown to be much faster than the other point iterative methods in solving the elliptic partial differential equations (EPDEs), which is due to the formers’ overall lower computational complexities. This paper is concerned with the application of a suitable Explicit Group (EG) iterative method for solving EPDEs. This study will compare several iterative methods such that S5-point-SOR,4 Point-EGSOR, 5S-point-AOR, and 4 Point-EGAOR. Numerical experiments were carried out to confirm our results by using MATLAB software. The results reveal that 4 Point-EGAOR is the most superior method among these methods.

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