Article
Mathematics, Applied
Rashid Ali, Ali Akgul
Summary: This study introduces and analyzes a new generalized accelerated overrelaxation method (NGAOR) for solving linear complementarity problems (LCPs), and proves the convergence of the method under certain conditions. Numerical experiments demonstrate the effectiveness and efficiency of the proposed method.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Multidisciplinary Sciences
Shiliang Wu, Cuixia Li, Praveen Agarwal
Summary: In this paper, a new equivalent fixed-point form of the linear complementarity problem is obtained by introducing a relaxed matrix, and a class of relaxed modulus-based matrix splitting iteration methods is established to solve the problem. Sufficient conditions for ensuring the convergence of relaxed modulus-based matrix splitting iteration methods are provided, and numerical examples are used to demonstrate the effectiveness of the proposed methods.
Article
Mathematics, Applied
Chen-Can Zhou, Qin-Qin Shen, Geng-Chen Yang, Quan Shi
Summary: This paper investigates an iteration method for large sparse quasi-complementarity problems (QCP) and proposes a general matrix splitting (MMS) iteration method to improve the convergence rate. The convergence analyses are conducted when the system matrix is either an H+-matrix or a positive definite matrix. Numerical experiments show that the proposed method outperforms the MMS iteration method.
Article
Mathematics, Applied
Cui-Xia Li, Shi-Liang Wu
Summary: This paper proposes a class of modulus-based matrix splitting methods for solving the complex linear complementarity problem (CLCP) by expressing it as equivalent absolute value equations. Sufficient conditions for the convergence of the proposed methods are provided, and numerical examples are presented to demonstrate their feasibility and efficiency.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Software Engineering
Cuixia Li, Shiliang Wu
Summary: This paper introduces a new method for solving the vertical linear complementarity problem (VLCP) and confirms its efficiency and superiority through numerical experiments.
OPTIMIZATION METHODS & SOFTWARE
(2023)
Article
Mathematics, Applied
Shiliang Wu, Liang Li
Summary: In this paper, a new modulus-based matrix splitting method is proposed for solving the implicit complementarity problem. The convergence of the method is guaranteed under certain conditions, which are presented in the paper. Numerical examples demonstrate the efficiency of the proposed method.
NUMERICAL ALGORITHMS
(2022)
Article
Operations Research & Management Science
Shiliang Wu, Cuixia Li
Summary: In this paper, a new modulus-based matrix splitting method is proposed for solving the linear complementarity problem economically and quickly. Numerical examples demonstrate the effectiveness of this method. Results also show that this new method is computationally more efficient compared to other existing methods.
OPTIMIZATION LETTERS
(2022)
Article
Operations Research & Management Science
Cui-Xia Li, Shi-Liang Wu
Summary: In this paper, a class of modulus-based matrix splitting iteration methods is proposed for solving the vertical linear complementarity problem (VLCP). The convergence properties of the proposed methods are discussed in depth. Numerical experiments confirm the efficiency of the proposed methods, showing that they are superior to the classical modulus-based matrix splitting iteration methods.
Article
Mathematics, Applied
Dong-Kai Li, Li Wang, Yu-Ying Liu
Summary: In this paper, we propose a relaxation general two-sweep matrix splitting iteration method for the linear complementarity problem. Convergence analysis demonstrates that the method converges to the exact solution of the linear complementarity problem when the system matrix is an H+-matrix. Numerical experiments show that the proposed method is more efficient than existing methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Dongmei Yu, Yiming Zhang, Cairong Chen, Deren Han
Summary: A new relaxed acceleration two-sweep modulus-based matrix splitting (NRATMMS) iteration method is developed for solving linear complementarity problems. The convergence of the NRATMMS method is established with the system matrix A being an H+-matrix. Numerical experiments show that the proposed method is superior to some existing algorithms under appropriate conditions.
Article
Mathematics, Applied
Jiewen He, SeakWeng Vong
Summary: A new kind of modulus-based matrix splitting methods is proposed in this paper to solve the vertical linear complementarity problems directly. The methods are different from existing formulations and their convergence is proven under certain conditions. Numerical experiments demonstrate the efficiency of the new methods.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
Yu-Jiang Wu, Wei-Hong Zhang, Ai-Li Yang
Summary: By formulating the large sparse linear complementarity problem as implicit fixed-point equations, a modulus-based iteration method is established with the assistance of an inexact non-alternating preconditioned matrix splitting iteration method. The convergence properties of this method are carefully demonstrated under certain conditions, and numerical results validate its superiority over other iteration methods in terms of iteration steps and computing times.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
Fang Chen, Yu Zhu
Summary: Based on a variational optimization model and physical constraints, this study establishes the equivalence between the Retinex problem and a linear complementarity problem. By solving an equivalent fixed-point equation, the solution of the Retinex problem can be computed. A variant of the two-step modulus-based matrix splitting iteration method is proposed and its unconditional convergence is proven. Numerical results demonstrate the effectiveness of this method in terms of iteration steps, computing time, and natural image quality evaluator.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Fang Chen, Yu Zhu, Galina V. Muratova
Summary: The Retinex theory proposes that an object's color is determined by its reflection ability to different wavelengths of light, rather than the intensity of the reflected light. The main goal of Retinex theory is to recover the true colors of objects from images. A new two-step modulus-based matrix splitting iteration method is proposed in this study to solve the Retinex problem, showing faster convergence speeds and significant improvement in reflectance recovery quality compared to existing methods.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics
Ximing Fang, Shouzhong Fu, Ze Gu
Summary: This paper discusses the conditions of modulus-based iteration methods based on the relationship between the linear complementarity problem and its reformulated fixed-point equation. It also presents convergence results on the two-step modulus-based matrix splitting iteration method with an H+-matrix, and provides numerical experiments.
