A general modulus-based matrix splitting method for linear complementarity problems of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>H</mml:mi></mml:math>-matrices

Li, Wen

doi:10.1016/j.aml.2013.06.015

Cited by 111 publications

(31 citation statements)

References 10 publications

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“…where u = 2 ((I − Ω −1 A)z − Ω −1 q) , Ω is an n × n positive diagonal matrix and is a positive constant. It also provides a universal framework for the iterative methods of LCP(q, A), for several instances, including a preconditioned modulus-based matrix splitting iteration method [19], a two-step modulus-based matrix splitting iteration method [31], a general modulus-based matrix splitting iteration method [18], an accelerated modulus-based matrix splitting iteration method [33] and so on.…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Jia

Wang

Xiao

2019

Commun. Appl. Math. Comput.

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In this paper, by means of constructing the linear complementarity problems into the corresponding absolute value equation, we raise an iteration method, called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method, for solving the linear complementarity problems whose coefficient matrix in ℝ n×n is large sparse and positive definite. From the convergence analysis, it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions. Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

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Section: Introductionmentioning

confidence: 99%

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Jia

Wang

Xiao

2019

Commun. Appl. Math. Comput.

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“…Zhang and Ren generalized the compatible H-splitting condition to an H-splitting [15]. L generalized modulus-based splitting iterative method to more general situationi [16]. Zhang et al studied the wider convergence when system matrix is an H + -matrix [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Global Modulus-Based Synchronous Multisplitting Multi-Parameters TOR Methods for Linear Complementarity Problems

Zhang

2017

MCA

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Abstract:In 2013, Bai and Zhang constructed modulus-based synchronous multisplitting methods for linear complementarity problems and analyzed the corresponding convergence. In 2014, Zhang and Li studied the weaker convergence results based on linear complementarity problems. In 2008, Zhang et al. presented global relaxed non-stationary multisplitting multi-parameter method by introducing some parameters. In this paper, we extend Bai and Zhang's algorithms and analyze global modulus-based synchronous multisplitting multi-parameters TOR (two parameters overrelaxation) methods. Moverover, the convergence of the corresponding algorithm in this paper are given when the system matrix is an H + -matrix.

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“…Recently, Bai [6] presented a modulus-based matrix splitting method which not only included the modified modulus method [7] and the nonstationary extrapolated modulus algorithms [8] as its special cases, but also yielded a series of iteration methods, such as modulusbased Jacobi, Gauss-Seidel, SOR and AOR iteration methods, which were extended to more general cases by Li [9]. In addition, Hadjidimos et al [10] and Zhang [11] proposed scaled extrapolated modulus algorithms and two-step modulus-based matrix splitting iteration methods, respectively.…”

Section: Introductionmentioning

confidence: 99%

The modulus-based nonsmooth Newton’s method for solving linear complementarity problems

Zheng

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tAs applying the nonsmooth Newton's method to the equivalent reformulation of the linear complementarity problem, a modulus-based nonsmooth Newton's method is established and its locally quadratical convergence conditions are presented. In the implementation, local one step convergence is discussed by properly choosing the initial vector and the generalized Jacobian, and a mixed algorithm is given for finding an initial vector. Numerical experiments show that the proposed methods are efficient and accelerate the convergence performance of the modulus-based matrix splitting iteration methods.

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A general modulus-based matrix splitting method for linear complementarity problems ofH-matrices

Cited by 111 publications

References 10 publications

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Global Modulus-Based Synchronous Multisplitting Multi-Parameters TOR Methods for Linear Complementarity Problems

The modulus-based nonsmooth Newton’s method for solving linear complementarity problems

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