In this work, a modulus-based inner-outer iteration method for solving a class of large sparse nonlinear complementarity problems with weak nonlinearity is constructed. The convergence of the proposed method is analyz...
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In this work, a modulus-based inner-outer iteration method for solving a class of large sparse nonlinear complementarity problems with weak nonlinearity is constructed. The convergence of the proposed method is analyzed when the system matrix is assumed to be an 1I+-matrix. Some numerical examples are presented to show that the proposed method can converge faster than the existing modulus-based matrix splitting iteration method.
By applying the Newton's iteration to the equivalent modulus equations of the nonlinear complementarity problems of P-matrices, a modulus-based nonsmooth Newton's method is established. The nearly quadratic co...
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By applying the Newton's iteration to the equivalent modulus equations of the nonlinear complementarity problems of P-matrices, a modulus-based nonsmooth Newton's method is established. The nearly quadratic convergence of the new method is proved under some assumptions. The strategy of choosing the initial iteration vector is given, which leads to a modified method. Numerical examples show that the new methods have higher convergence precision and faster convergence rate than the known modulus-based matrix splitting iteration method.
In this paper, a general accelerated modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods and the accelerated modulus-based ma...
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In this paper, a general accelerated modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods and the accelerated modulus-based matrix splitting iteration methods. The convergence analysis is given when the system matrix is an -matrix. Numerical examples show that the proposed methods are efficient and accelerate the convergence performance with less iteration steps and CPU times.
In this paper, the relaxation modulus-based matrix splitting iteration method is established for solving the linear complementarity problem of positive definite matrices. The convergence analysis and the strategy of t...
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In this paper, the relaxation modulus-based matrix splitting iteration method is established for solving the linear complementarity problem of positive definite matrices. The convergence analysis and the strategy of the choice of the parameters are given. Numerical examples show that the proposed method with the new strategy is efficient and accelerates the convergence performance with less iteration steps and CPU times. (C) 2017 Elsevier Inc. All rights reserved.
Linear complementarity problems have drawn considerable attention in recent years due to their wide *** this article,we introduce the two-step two-sweep modulus-based matrix splitting(TSTM)iteration method and two-swe...
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Linear complementarity problems have drawn considerable attention in recent years due to their wide *** this article,we introduce the two-step two-sweep modulus-based matrix splitting(TSTM)iteration method and two-sweep modulus-based matrix splitting type II(TM II)iteration method which are a combination of the two-step modulus-based method and the two-sweep modulus-based method,as two more effective ways to solve the linear complementarity *** convergence behavior of these methods is discussed when the system matrix is either a positive-definite or an H+-***,numerical experiments are given to show the efficiency of our proposed methods.
In this paper, the modulus-based matrix splitting (MMS) iteration method is extended to solve the horizontal quasi-complementarity problem (HQCP), which is characterized by the presence of two system matrices and two ...
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In this paper, the modulus-based matrix splitting (MMS) iteration method is extended to solve the horizontal quasi-complementarity problem (HQCP), which is characterized by the presence of two system matrices and two nonlinear functions. based on the specific matrix splitting of the system matrices, a series of MMS relaxation iteration methods are presented. Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H+-matrices, respectively. Finally, two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.
based on the two-sweep modulus-based matrix splitting iteration (TMMS) method for linear complementarity problems developed by Wu and Li (Comput. Appl. Math. 302: 327-339, 2016), a new generalized variant of the TMMS ...
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based on the two-sweep modulus-based matrix splitting iteration (TMMS) method for linear complementarity problems developed by Wu and Li (Comput. Appl. Math. 302: 327-339, 2016), a new generalized variant of the TMMS (GTMMS) method is put forth for solving horizontal linear complementarity problems. By analyzing the convergence of the proposed method, we attain its convergence conditions. The results of numerical experiments not only indicate that the convergence of the proposed method is better, but also analyze and provide the relevant factors affecting the convergence.
In this paper, a modified modulus-based matrix splitting iteration method is established for solving a class of implicit complementarity problems. The global convergence conditions are given when the system matrix is ...
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In this paper, a modified modulus-based matrix splitting iteration method is established for solving a class of implicit complementarity problems. The global convergence conditions are given when the system matrix is a positive definite matrix or an H+-matrix, respectively. In addition, some numerical examples show that the proposed method is efficient.
In this paper, first we propose a general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems. In order to improve the computing efficiency, we further propose a prec...
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In this paper, first we propose a general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems. In order to improve the computing efficiency, we further propose a preconditioned general modulus-based matrix splitting iteration method. We establish the convergence theorems when the coefficient matrices are (symmetric) positive definite matrices and H+-matrices, respectively. Numerical results show that the proposed preconditioned general modulus-based matrix splitting iteration method is superior than some existing methods and the general modulus-based matrix splitting iteration method.
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...
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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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