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Keywords = HSS iterative method

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24 pages, 1524 KB  
Article
A Data-Driven Parameter Prediction Method for HSS-Type Methods
by Kai Jiang, Jianghao Su and Juan Zhang
Mathematics 2022, 10(20), 3789; https://doi.org/10.3390/math10203789 - 14 Oct 2022
Viewed by 2152
Abstract
Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice of these parameters directly affects the efficiency of the corresponding iterative methods. This paper uses a Bayesian inference-based Gaussian process regression [...] Read more.
Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice of these parameters directly affects the efficiency of the corresponding iterative methods. This paper uses a Bayesian inference-based Gaussian process regression (GPR) method to predict the relatively optimal parameters of some HSS-type iteration methods and provide extensive numerical experiments to compare the prediction performance of the GPR method with other existing methods. Numerical results show that using GPR to predict the parameters of the matrix-splitting iterative methods has the advantage of smaller computational effort, predicting more optimal parameters and universality compared to the currently available methods for finding the parameters of the HSS-type iteration methods. Full article
(This article belongs to the Special Issue Matrix Equations and Their Algorithms Analysis)
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17 pages, 294 KB  
Article
An Efficient Iterative Method Based on Two-Stage Splitting Methods to Solve Weakly Nonlinear Systems
by Abdolreza Amiri, Mohammad Taghi Darvishi, Alicia Cordero and Juan Ramón Torregrosa
Mathematics 2019, 7(9), 815; https://doi.org/10.3390/math7090815 - 3 Sep 2019
Cited by 3 | Viewed by 2986
Abstract
In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that [...] Read more.
In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that any faster and less time-consuming two-stage splitting method that satisfies the convergence theorem can be replaced instead of the HSS inner iterations. Numerical results, such as CPU time, show the robustness of our new method. This method is easy, fast and convenient with an accurate solution. Full article
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
13 pages, 241 KB  
Article
PHSS Iterative Method for Solving Generalized Lyapunov Equations
by Shi-Yu Li, Hai-Long Shen and Xin-Hui Shao
Mathematics 2019, 7(1), 38; https://doi.org/10.3390/math7010038 - 3 Jan 2019
Cited by 6 | Viewed by 2774
Abstract
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 [...] Read more.
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. Full article
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