Journal Article10.1016/J.APNUM.2020.09.008
A modified modulus-based multigrid method for linear complementarity problems arising from free boundary problems
Li-Li Zhang,Zhi-Ru Ren +1 more
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TL;DR: A modified modulus-based multigrid method is presented to solve the linear complementarity problem arising from a free boundary problem as a fixed-point equation and is a standard full approximation scheme, which makes it more convenient and efficient in practical applications.
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About: This article is published in Applied Numerical Mathematics. The article was published on 01 Jun 2021. The article focuses on the topics: Multigrid method & Rate of convergence.
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Citations
A general modulus-based matrix splitting method for quasi-complementarity problem
TL;DR: For large sparse quasi-complementarity problem (QCP), Wu and Guo recently studied a modulus-based matrix splitting (MMS) iteration method, and the results indicate that the new proposed GMMS method achieves a better performance than the MMS iteration method.
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Solution of Tensor Complementarity Problem Using Homotopy Function
A. Dutta,Bharat Kumar,Deepmala,A. K. Das +3 more
- 04 May 2022
TL;DR: In this article , a homotopy continuation method is proposed to solve the tensor complementarity problem under some conditions, which is a subclass of nonlinear complementarity problems for which the involved function is defined by a tensor.
•Posted Content
Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems
TL;DR: In this article, a homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem of the original linear complementarity problem is proposed.
Modulus-Based Cascadic Multigrid Method for Quasi-variational Inequality Problems
Katelyn Gao,Chenliang Li +1 more
Numerical efficiency of modified modulus-based multigrid cycles with application to free boundary problems
TL;DR: In this article, a modified modulus-based multigrid method is applied to solve free boundary problems, and the modified V-cycle does not show a grid-independence convergence rate.
References
•Book
The Linear Complementarity Problem
Richard W. Cottle,Jong-Shi Pang,Richard Stone +2 more
- 18 Feb 1992
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
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Engineering and Economic Applications of Complementarity Problems
Michael C. Ferris,Jong-Shi Pang +1 more
TL;DR: The goal of this documentation is to summarize the essential applications of the nonlinear complementarity problem known to date, to provide a basis for the continued research on the non linear complementarityproblem, and to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation
TL;DR: In this article, the authors consider the problem of finding real column n-vectors in a real symmetric positive definite matrix, where the columns of the matrix are real column vectors.
Modulus‐based matrix splitting iteration methods for linear complementarity problems
TL;DR: Numerical results show that the modulus-based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency.
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A modified modulus method for symmetric positive‐definite linear complementarity problems
Jun-Liang Dong,Mei-Qun Jiang +1 more
Abstract: By reformulating the linear complementarity problem into a new equivalent fixed‐point equation, we deduce a modified modulus method, which is a generalization of the classical one. Convergence for this new method and the optima of the parameter involved are analyzed. Then, an inexact iteration process for this new method is presented, which adopts some kind of iterative methods for determining an approximate solution to each system of linear equations involved in the outer iteration. Global convergence for this inexact modulus method and two specific implementations for the inner iterations are discussed. Numerical results show that our new methods are more efficient than the classical one under suitable conditions. Copyright © 2008 John Wiley & Sons, Ltd.
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