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.

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 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.

NEW THREE-STEP ITERATIVE METHOD FOR SOLVING MIXED VARIATIONAL INEQUALITIES

2011 ◽  
Vol 08 (01) ◽  
pp. 139-150
Author(s):  
ABDELLAH BNOUHACHEM ◽  
MUHAMMAD ASLAM NOOR ◽  
ZHAOHAN SHENG ◽  
EISA AL-SAID
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Numerical Experiments ◽  
New Method ◽  
Descent Direction ◽  
Mild Conditions ◽  
Globally Convergent ◽  
Special Cases ◽  
Mixed Variational Inequalities

In this paper, we suggest and analyze a new three-step iterative method for solving mixed variational inequalities. The new iterate is obtained by using a descent direction. We prove that the new method is globally convergent under suitable mild conditions. Our results can be viewed as significant extensions of the previously known results for mixed variational inequalities. Since mixed variational inequalities include variational inequalities as special cases, our method appears to be a new one for solving variational inequalities. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.

scholarly journals Convergent Homotopy Analysis Method for Solving Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
H. Nasabzadeh ◽  
F. Toutounian
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Iterative Methods ◽  
Homotopy Analysis Method ◽  
Numerical Experiments ◽  
Series Solution ◽  
Iterative Scheme ◽  
New Method ◽  
Analysis Method ◽  
Homotopy Analysis

By using homotopy analysis method (HAM), we introduce an iterative method for solving linear systems. This method (HAM) can be used to accelerate the convergence of the basic iterative methods. We also show that by applying HAM to a divergent iterative scheme, it is possible to construct a convergent homotopy-series solution when the iteration matrix G of the iterative scheme has particular properties such as being symmetric, having real eigenvalues. Numerical experiments are given to show the efficiency of the new method.

scholarly journals On preconditioned normal and skew-Hermitian splitting iteration method for continuous Sylvester equations AX + XB = C*

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2207-2217
Author(s):  
Xue-Qing Liang ◽  
Xiang Wang ◽  
Xiao-Bin Tang ◽  
Xiao-Yong Xiao
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Property ◽  
Positive Definite ◽  
New Method ◽  
Splitting Iteration Method

In this paper, we present a preconditioned normal and skew-Hermitian splitting (PNSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. Theoretical analysis shows that the PNSS methods will converge unconditionally to the exact solution of the continuous Sylvester equations. An inexact variant of the PNSS iteration method(IPNSS) and the analysis of its convergence property in detail have been established. Numerical experiments further show that this new method is more efficient and robust than the existing ones.

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