Journal ArticleDOI
On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem
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TLDR
The convergence properties of a variant of the multisplitting methods for solving the large sparse linear complementarity problems presented by Machida, Fukushima, and Ibaraki are further discussed when the system matrices are nonsymmetric and the weightingMatrices are nonnegative and diagonal.Abstract:
The convergence properties of a variant of the multisplitting methods for solving the large sparse linear complementarity problems presented by Machida, Fukushima, and Ibaraki [J. Comput. Appl. Math., 62 (1995), pp. 217--227] are further discussed when the system matrices are nonsymmetric and the weighting matrices are nonnegative and diagonal. This directly results in several novel sufficient conditions for guaranteeing the convergence of these multisplitting methods. Moreover, some applicable parallel multisplitting relaxation methods and their corresponding convergence properties are discussed in detail.read more
Citations
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Journal ArticleDOI
Rigid-Body Dynamics with Friction and Impact
TL;DR: This paper presents rigorous results about rigid-body dynamics with Coulomb friction and impulses, which have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L.
Journal ArticleDOI
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.
Journal ArticleDOI
A modified modulus method for symmetric positive‐definite linear complementarity problems
Jun-Liang Dong,Mei-Qun Jiang +1 more
Journal ArticleDOI
Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem
Ning Zheng,Jun-Feng Yin +1 more
TL;DR: Numerical experiments show that the proposed methods are efficient and accelerate the convergence performance of the modulus-based matrix splitting iteration methods with less iteration steps and CPU time.
Journal ArticleDOI
Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems
Zhong-Zhi Bai,Li-Li Zhang +1 more
TL;DR: Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation and improve the existing convergence theory.
References
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Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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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
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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.
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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.