Journal Article10.1007/S11075-020-00954-1
A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems
Hua Zheng,Seakweng Vong +1 more
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TL;DR: The convergence analysis of the proposed two-step modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems is presented, including the case of accelerated overrelaxation splitting.
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Abstract: In this paper, for solving horizontal linear complementarity problems, a two-step modulus-based matrix splitting iteration method is established. The convergence analysis of the proposed method is presented, including the case of accelerated overrelaxation splitting. Numerical examples are reported to show the efficiency of the proposed method.
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Citations
A generalization of irreducibility and diagonal dominance with applications to horizontal and vertical linear complementarity problems
TL;DR: In this article, the authors generalize and analyze the concepts of diagonal dominance and irreducibility in the framework of column and row representative matrices of a set, including the definition of particular sets of M- and H-matrices.
17
On the modulus-based successive overrelaxation iteration method for horizontal linear complementarity problems arising from hydrodynamic lubrication
Hua Zheng,Seakweng Vong +1 more
TL;DR: In this paper, the convergence of modulus-based successive overrelaxation iteration method is presented, which extends the existing results given in the recent work of Mezzadri F. and Galligani E.
9
A two-step new modulus-based matrix splitting method for vertical linear complementarity problem
Cuixia Li,Shiliang Wu +1 more
TL;DR: A two-step modulus-based matrix splitting method is introduced for solving the vertical linear complementarity problem, with convergence properties discussed and numerical experiments confirming its superiority over existing methods.
3
A generalized variant of two-sweep modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems
TL;DR: The results of numerical experiments indicate that the convergence of the proposed method is better, but also analyze and provide the relevant factors affecting the convergence.
3
References
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Abraham Berman
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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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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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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.
335
Convergence of relaxed parallel multisplitting methods
Andreas Frommer,Günter Mayer +1 more
TL;DR: This work investigates two different variants of relaxed multisplitting methods, if A is an H-matrix, these methods converge if the relaxation parameter is from an interval (0,ω0) with ω0 > 1.
249
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.
150