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A CLASS OF GENERALIZED MULTISPLITTING RELAXATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Applied Mathematics(A Journal of Chinese Universities) 1998年第2期13卷 188-198页

作者： BAI ZHONGZHI State Key Laboratory of Scientfic/Engineering Computing Institute of Computational Mathemstics and Scientific/Engineering ComputingChinese Academy of Sciences Beijing

Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set *** class of methods not only includes all the existing relaxation methods for the linear complementarity problems,but also yields a lot of novel ones in the sense of *** establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H matrix with positive diagonal elements.

关键词： Linear complementarity problem matrix multisplitting relaxation method convergnece theory

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A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains

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LINEAR ALGEBRA AND ITS APPLICATIONS 1997年第0期266卷 219-241页

作者： Bai, ZZ State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 P. R. China

Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations. Various iterative methods have been proposed to determine the matrices of interest. We propose a new, efficient successive-substitution Moser method and a Newton-Moser method which use the Moser formula (which, originally, is just the Schulz method). These new methods avoid the inverses of the matrices, and thus considerable savings on the computational workloads may be achieved. Moreover, they are much more suitable for implementing on parallel multiprocessor systems. Under certain conditions, we establish monotone convergence of these new methods, and prove local linear convergence for the substitution Moser method and superlinear convergence for the Newton-Moser method. (C) 1997 Elsevier Science Inc.

关键词： Queuing theory Probability queueing theory nonlinear equations Markov new methods monotone convergence iterative methods Markov chain

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Comparative study on order-reduced methods for linear third-order ordinary differential equations

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Frontiers of Mathematics in China 2012年第6期7卷 1151-1168页

作者： Zhiru REN State Key Laboratory of Scientific/Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering Computing Academy of Mathematics andSystems Science Chinese Academy of Sciences P. O. Box 2719 Beijing 100190 China

The linear third-order ordinary differential equation （ODE） can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions p（z） and q（x） in the variable replacement to get different cases of the special order-reduced system for the linear third-order ODE. We analyze the numerical behavior and algebraic properties of the systems of linear equations resulting from the sine diseretizations of these special second-order ODE systems. Then the block-diagonal preconditioner is used to accelerate the convergence of the Krylov subspace iteration methods for solving the discretized system of linear equation. Numerical results show that these order-reduced methods are effective for solving the linear third-order ODEs.

关键词： third-order ordinary differential equation order-reduced method sine discretization preeonditioner Krylov subspace method

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Parallel hybrid algebraic multilevel iterative methods

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LINEAR ALGEBRA AND ITS APPLICATIONS 1997年第1-3期267卷 281-315页

For the large-scale system of linear equations with symmetric positive definite block coefficient matrix resulting from the discretization of a self-adjoint elliptic boundary-value problem, by making use of the blocked multilevel iteration idea, we construct preconditioning matrices for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iterative methods for solving this kind of system of linear equations. Theoretical analysis shows that not only do these new methods lend themselves to parallel computation, but also their convergence rates are independent of both the sizes and the level numbers of the grids, and their computational work loads are also hounded by linear functions of the step sizes of the finest grids. (C) 1997 Elsevier Science Inc.

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A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING

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Journal of Computational Mathematics 2001年第3期19卷 309-322页

作者： Xin-wei Liu Ya-xiang Yuan State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100080China Faculty of Science and Arts Hebei University of TechnologyTianjin 300130China

Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N... 详细信息

关键词： trust region algorithm nonlinear programming

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A NEW ADAPTIVE SUBSPACE MINIMIZATION THREE-TERM CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2021年第2期39卷 159-177页

作者： Keke Zhang Hongwei Liu Zexian Liu School of Mathematics and Statistics Xidian UniversityXi’an 710126China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computingAMSSChinese Academy of SciencesBeijing 100190China

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this *** search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each *** obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent *** the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild *** experiments show that the proposed algorithm is promising for the given test problem set.

关键词： Conjugate gradient method Nonmonotone line search Subspace minimization Sufficient descent condition Global convergence

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Sparse two-sided rank-one updates for nonlinear equations

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Science China Mathematics 2010年第11期53卷 2907-2915页

作者： CHENG MingHou & DAI YuHong state key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented.

关键词： TR1 update Broyden rank-one update sparsity

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TETRAHEDRAL C^m INTERPOLATION BY RATIONAL FUNCTIONS

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Journal of Computational Mathematics 2001年第2期19卷 131-138页

作者： Guo-liang Xu Chuan I Chu Wei-min Xue State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics an d Systems SciencesChinese Academy of SciencesBeijing 100080China Department of Mathematics Hong Kong Baptist UniversityKowloonHong Kong

A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.

关键词： C-m interpolation rational functions tetrahedra

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Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

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Science China(Physics,Mechanics & Astronomy) 2018年第1期61卷 57-67页

作者： XiaoXu Zhong ShiJun Liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration State Key Laboratory of Ocean Engineering Ministry-of-Education Key Laboratory of Scientific and Engineering Computing

Analytic approximations of the Von Karman＇s plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method （HAM）, an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c1 and c2 in the frame of the HAM. Besides, it is found that the HAM- based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c1= -0 and c2 = -1, where 0 denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c1 = -0 and c2= -1. In addition, we prove that the HAM approach for the Von karman＇s plate equations in differential form is just a special case of the HAM for the Von karman＇s plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

关键词： circular plate high nonlinearity homotopy analysis method

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Lie Point Symmetries of Differential-Difference Equations

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Communications in Theoretical Physics 2004年第5期41卷 645-648页

作者： DING Wei~1 TANG Xiao-Yan~(2,3) 1 Department of Applied Mathematics,Shanghai Jiao Tong University,Shanghai 200030,China2 Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China3 state key laboratory of scientific and engineering computing,Institute of Computational Mathematics and scientific engineering computing,Academy of Mathematics and System Sciences,the Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

In this paper,the classical Lie group approach is extended to find some Lie point symmetries of differential-difference *** reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

关键词： Lie point symmetry differential-difference equation Kac Moody-Virasoro algebra

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