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SOME NONLINEAR APPROXIMATIONS FOR MATRIX-VALUED FUNCTIONS

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Journal of Computational mathematics 2003年第6期21卷 801-814页

作者： Guo-liang Xu(academy of mathematics and System {2.s, chinese academy of {2.s,beijing 100080, china) academy of mathematics and System {2.s Chinese Academy of Sciences 北京 100080

Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2.-type and (1,2.-type fraction-sum approximations, for matrix-valued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed. Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.

关键词： Matrix-valued function Nonlinear approximation Interpolation.

Matrix expression and reachability analysis of finite automata

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控制理论与应用（英文版） 2012年第2期10卷 210-215页

作者： Xiangru XU, Yiguang HONG Key Laboratory of systems and Control, academy of {2. and systems science, chinese academy of sciences, beijing 100190, china Key Laboratory of systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.

关键词： Finite automata Reachability Matrix expression Semitensor product

OPTIMAL MIXED H-P FINITE ELEMENT METHODS FOR STOKES AND NON-NEWTONIAN FLOW

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Journal of Computational mathematics 2001年第1期19卷 67-76页

作者： Ping-bing Ming Zhong-ci Shi (Institute of Computational mathematics, chinese {2. of sciences, beijing 100080, china) 中科院计算数学与工程计算数学所北京 100080

Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H... 详细信息

关键词： mixed hp- finite element method non-Newtonian flow stabilization scaled weak B-Binequality

MATHEMATICAL ANALYSIS FOR QUADRILATERAL ROTATED Q_1 ELEMENT Ⅲ: THE EFFECT OF NUMERICAL INTEGRATION

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Journal of Computational mathematics 2003年第3期21卷 287-294页

作者： Ping-bing Ming Zhong-ci Shi (Institute of Computational mathematics, chinese {2. of sciences, beijing 100080, china) Institute of Computational mathematics Chinese Academy of Sciences 北京 100080

This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a Q1 unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

关键词： Quadrilateral rotated Q1 element Numerical quadrature.

Precise Asymptotics of Error Variance Estimator in Partially Linear Models

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 59-74页

作者： Shao-jun Guo, Min Chen, Feng Liu academy of mathematics and {2. science, chinese academy of sciences, beijing 100080, china Department of Statistics, Chongqing Institute of Technology, Chongqing 630000, china academy of mathematics and {2. science Chinese Academy of Sciences Beijing China Department of Statistics Chongqing Institute of Technology Chongqing China

In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, yi = xiτβ+ g(ti) +εi, 1≤i≤n, {εi,i = 1,…, n} are i.i.d random errors with mean 0 and positive finite varianceσ2. Following the ideas of Allan Gut and Aurel Spatarut and Zhang, on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.

关键词： Precise asymptotics partially linear models error variance estimator

PROJECTION-PURSUIT BASED PRINCIPAL COMPONENT ANALYSIS:A LARGE SAMPLE THEORY

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同方期刊数据库

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Journal of systems science & Complexity 2006年第3期19卷 365-385页

作者： Jian ZHANG Institute of mathematics,Statistics and Actuarial science,University of Kent,Canterbury,Kent CT2.7NF,U.K. Institute of {2. science,academy of mathematics and {2. science,chinese academy of sciences,beijing 100080,{12. Institute of mathematics Statistics and Actuarial Science University of Kent Canterbury Institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences

The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.

关键词： Dispersion matrices eigenvalues and eigenvectors empirical processes principal component analysis projection pursuit (PP).

Subspace Search Method for Quadratic Programming With BoxConstraints

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Journal of Computational mathematics 1999年第3期17卷 307-314页

作者： Zi-luan Wei(ICMSEC, chinese academy of {2.s, beijing 100080, china) 中科院计算数学与科学工程计算所北京

A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.

关键词： subspace search method quadratic programing matrix splitting

Gasdynamic characteristics of toroidal shock and detonation wave converging

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science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 739-749页

作者： TENG Honghui1,2.& JIANG Zonglin2.1. Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, chinese academy of Sci- ences, {2., china 2. Graduate University of chinese academy of sciences, beijing 100039, china Key Laboratory of High Temperature Gas Dynamics Institute of Mechanics Chinese Academy of Sciences Beijing China Graduate University of chinese academy of {2.s Beijing China

The modified CCW relation is applied to analyzing the shock, detonation wave converging and the role of chemical reactions in the process. Results indicate that the shock wave is strengthened faster than the detonation wave in the converging at the same initial Mach number. Euler equations implemented with a detailed chemical reaction model are solved to simulate toroidal shock and detonation wave converging. Gasdynamic characteristics of the converging are investigated, including wave interaction patterns, observable discrepancies and physical phenomena behind them. By comparing wave diffractions, converging processes and pressure evolutions in the focusing area, the different effects of chemical reactions on diffracting and converging processes are discussed and the analytic conclusion is demonstrated through the observation of numerical simulations.

关键词： converging, CCW relation, shock wave, detonation wave.

Integrated precise orbit determination of Shenzhou IV unmanned spacecraft

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science china(Technological sciences) 2004年第5期47卷 518-525页

作者： L Congmin1,2. GU Yidong3, LIN Baojun3 & GUO Jiong3 1. Center for Space science and Applied Research, chinese {2. of sciences, beijing 100080, china 2. Graduate School of the chinese {2. of sciences, beijing 100039, china 3. General Establishment of Space science and Application, chinese {2. of sciences, beijing 100080, china Correspondence should be addressed to L Congmin General Establishment of Space science and Application Chinese Academy of Sciences

Considering the characteristic orbit of Shenzhou IV spacecraft and the advantages and disadvantages of several types of domestic orbit measurements, a scheme of IPOD is determined, which uses GPS, SLR and USB observation data jointly plus precise ionosphere corrections to GPS observation data. IPOD system and mathematic models of OD are introduced. The results of different joint OD are analyzed using true observation data, and show that radial accuracy is better than 2.m.

关键词： Shenzhou IV unmanned spacecraft integrated precise orbit determination GPS SLR USB.