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 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 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 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 Photoelastic Properties of Trigonal Crystals

Crystals ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1095
Author(s):  
Bohdan Mytsyk ◽  
Nataliya Demyanyshyn ◽  
Anatoliy Andrushchak ◽  
Oleh Buryy
Keyword(s):  
Elastic Stiffness ◽  
Interferometric Method ◽  
Absolute Value ◽  
Interferometric Technique ◽  
Stiffness Coefficients ◽  
Half Wave ◽  
Compliance Coefficient ◽  
The Matrix ◽  
The Absolute ◽  
The Right

All possible experimental geometries of the piezo-optic effect in crystals of trigonal symmetry are studied in detail through the interferometric technique, and the corresponding expressions for the calculation of piezo-optic coefficients (POCs) πim and some sums of πim based on experimental data obtained from the samples of direct and X/45°-cuts are given. The reliability of the values of POCs is proven by the convergence of πim obtained from different experimental geometries as well as by the convergence of some sums of POCs. Because both the signs and the absolute values of POCs π14 and π41 are defined by the choice of the right crystal-physics coordinate system, we here use the system whereby the condition S14 > 0 is fulfilled (S14 is an elastic compliance coefficient). The absolute value and the sign of S14 are determined by piezo-optic interferometric method from two experimental geometries. The errors of POCs are calculated as mean square values of the errors of the half-wave stresses and the elastic term. All components of the matrix of elasto-optic coefficients pin are calculated based on POCs and elastic stiffness coefficients. The technique is tested on LiTaO3 crystal. The obtained results are compared with the corresponding data for trigonal LiNbO3 and Ca3TaGa3Si2O14 crystals.

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 A modified AOR-type iterative method for L-matrix linear systems

2007 ◽  
Vol 49 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Shiliang Wu ◽  
Tingzhu Huang
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Rates ◽  
Comparison Theorems ◽  
Iterative Schemes ◽  
Seidel Method ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

AbstractBoth Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.

scholarly journals Constructing a High-Order Globally Convergent Iterative Method for Calculating the Matrix Sign Function

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Haifa Bin Jebreen
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Eighth Order ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Globally Convergent ◽  
The Matrix ◽  
Matrix Iteration ◽  
Particulate Matrix ◽  
Theoretical Results

This work is concerned with the construction of a new matrix iteration in the form of an iterative method which is globally convergent for finding the sign of a square matrix having no eigenvalues on the axis of imaginary. Toward this goal, a new method is built via an application of a new four-step nonlinear equation solver on a particulate matrix equation. It is discussed that the proposed scheme has global convergence with eighth order of convergence. To illustrate the effectiveness of the theoretical results, several computational experiments are worked out.

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.

Sign in / Sign up

Export Citation Format

Share Document