Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems
Li-Li Zhang,Zhi-Ru Ren +1 more
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TLDR
The convergence conditions of modulus-based matrix splitting and matrix two-stage splitting iteration methods for linear complementarity problems are weakened, and their applied scopes are further extended.About:
This article is published in Applied Mathematics Letters.The article was published on 2013-06-01 and is currently open access. It has received 76 citations till now. The article focuses on the topics: Matrix splitting & Convergent matrix.read more
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Matrix iterative analysis (2nd edn), by Richard S. Varga. Springer Series in Computational Mathematics 27. Pp. 358. £55. 2000. ISBN 3 540 66321 5 (Springer Verlag).
TL;DR: Roughly one in six of Walsh's 281 publications are included, photographically reproduced, and reproduction is excellent except for one paper from 1918, which is an obituary.
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A general modulus-based matrix splitting method for linear complementarity problems of H-matrices
TL;DR: The modulus-based matrix splitting iteration method is extended to more general cases, and then convergence analysis when the system matrix A is an H + -matrix is presented.
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A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems
Hua Zheng,Wen Li,Seakweng Vong +2 more
TL;DR: A relaxation modulus-based matrix splitting iteration method is established, which covers the known general modulus based matrix splitting iterations methods and is efficient and accelerate the convergence performance with less iteration steps and CPU times.
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Modulus-based matrix splitting methods for horizontal linear complementarity problems
TL;DR: Modulus-based matrix splitting iteration methods to horizontal linear complementarity problems are extended and both standard and accelerated methods are considered and their convergence is analyzed.
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A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices
TL;DR: In this paper, a preconditioned modulus-based iteration method for linear complementarity problems with the system matrix being an -matrix is presented, and the convergence analysis of the proposed method is given.
References
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Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Book
The Linear Complementarity Problem
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.
Journal ArticleDOI
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.
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Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem
Ning Zheng,Jun-Feng Yin +1 more