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 BAS iteration method for absolute value equation

2021 ◽  
Vol 7 (1) ◽  
pp. 606-616
Author(s):  
Cui-Xia Li ◽  
◽  
Long-Quan Yong ◽  
Keyword(s):  
Theoretical Analysis ◽  
Numerical Solution ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Speed ◽  
Absolute Value Equation ◽  
Absolute Value ◽  
The Absolute ◽  
Block Diagonal

<abstract><p>In this paper, to improve the convergence speed of the block-diagonal and anti-block-diagonal splitting (BAS) iteration method, we design a modified BAS (MBAS) method to obtain the numerical solution of the absolute value equation. Theoretical analysis shows that under certain conditions the MBAS method is convergent. Numerical experiments show that the MBAS method is feasible.</p></abstract>

scholarly journals PHSS Iterative Method for Solving Generalized Lyapunov Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 38 ◽  
Author(s):  
Shi-Yu Li ◽  
Hai-Long Shen ◽  
Xin-Hui Shao
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Lyapunov Equation ◽  
New Method ◽  
New Methods ◽  
Generalized Lyapunov Equation ◽  
Improvement Effect ◽  
Hss Iteration ◽  
Hss Iteration Method

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

A Shift Splitting Iteration Method for Generalized Absolute Value Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equations ◽  
Convergence Conditions ◽  
Absolute Value ◽  
Splitting Technique ◽  
Splitting Iteration Method ◽  
Generalized Absolute Value Equations

Abstract In this paper, based on the shift splitting technique, a shift splitting (SS) iteration method is presented to solve the generalized absolute value equations. Convergence conditions of the SS method are discussed in detail when the involved matrices are some special matrices. Finally, numerical experiments show the effectiveness of the proposed method.

scholarly journals PHSS Iterative Method for Solving Generalized Lyapunov Equations

2018 ◽  
Author(s):  
Shi-Yu Li ◽  
Hai-Long Shen ◽  
Xin-Hui Shao
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Lyapunov Equation ◽  
New Method ◽  
New Methods ◽  
Generalized Lyapunov Equation ◽  
Improvement Effect ◽  
Hss Iteration ◽  
Hss Iteration Method

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

scholarly journals On Picard-SHSS iteration method for absolute value equation

2021 ◽  
Vol 6 (2) ◽  
pp. 1743-1753
Author(s):  
Shu-Xin Miao ◽  
◽  
Xiang-Tuan Xiong ◽  
Jin Wen
Keyword(s):  
Iteration Method ◽  
Absolute Value Equation ◽  
Absolute Value

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.

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