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CONVERGENCE OF (0,1,2,3) INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

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Journal of Computational mathematics 2001年第2期19卷 151-156页

作者： Ying-guang Shi (institute of Computation, Hunan Normal University, Changsha 410081, china) (institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and systems sciences, chinese academy of sciences, beijing 100 湖南师范大学湖南长沙 410081

Provides information on a study which simplified and improved convergence of (0,1,2,3) interpolation on an arbitrary system of nodes. Definitions and notations; Results; Conjectures.

关键词： Hermite interpolation Hermite-Fejer interpolation convergence

On notions of harmonicity for non-symmetric Dirichlet form

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science china mathematics 2010年第6期53卷 1407-1420页

作者： MA ZhiMing1, ZHU RongChan1, & ZHU XiangChan2 1institute of applied mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china 2School of Mathematical sciences, Peking University, beijing 100871, china 1. institute of applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.

关键词： harmonic functions uniformly integrable martingale SPV integrable non-symmetric Dirichlet forms non-symmetric Beurling-Deny decomposition Hunt processes

The asymptotic stability of multistep multiderivative methods for systems of delay differential equations

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Communications in Nonlinear science and Numerical Simulation 2000年第1期5卷 24-26页

作者： Chengming HUANG and Qianshun CHANG institute of applied mathematics, chinese academy of sciences, P. O. Box 2734, beijing 100080, china institute of applied mathematics Chinese Academy of Sciences P. O. Box 2734 Beijing 100080 China

This paper deals with the asymptotic stability of multistep multiderivative methods for systems of delay differential equations. In particular, it is shown that A-stability of multistep multiderivative methods for ord... 详细信息

关键词： delay differential equation stability multistep multiderivative methods

ROBUST CONSENSUS AND SOFT CONTROL OF MULTI-AGENT systems WITH NOISES

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Journal of systems science & Complexity 2008年第3期21卷 406-415页

作者： Lin WANG Lei GUO institute of systems science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper considers the problem of robust consensus for a basic class of multi-agent systems with bounded disturbances and with directed information flow. A necessary and sufficient condition on the robust consensus is first presented, which is then applied to the analysis, control and decision making problems in the noise environments. In particular, the authors show how a soft control technique will synchronize a group of autonomous mobile agents without changing the existing local rule of interactions, and without assuming any kind of connectivity conditions on the system trajectories.

关键词： Directed graph robust consensus soft control time-varying systems

Absolute Stability of General Lurie Control systems with Multi-Nonlinear Feedback Terms

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Acta Mathematica Sinica,English Series 2001年第4期17卷 649-656页

作者： Zuo Xin GAN Wei Gao GE institute of systems science, chinese academy of sciences, beijing 100080, P. R. china Department of applied mathematics, beijing institute of Technology, beijing 100081, P. R. china institute of systems science Chinese Academy of Sciences Beijing 100080 P. R. China Department of applied mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper, the problenl of absohlte stability for general Lurie control systems with multi- nonlinear feedback terms is investigated. From the Lyapunov function approach. new necessary and sufficient conditious and some practical sufficient conditions of absolute stability are derived. which improve the absolute stability for the set. A numerical examplc illustrates the effectiveness of the proposed results.

关键词： General Lurie system Multi-nonlinear feedback Absolute stability

Two-dimensional Riemann problems of simplified Euler equation

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chinese science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2 and HUANG Feimin+1 1. institute of applied mathematics, chinese academy of sciences, beijing 100080, china 2. Department of mathematics, Shantou University, Guangdong 515063, china institute of applied mathematics Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

Existence of SURU estimators in SURE model with special covariance structures

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chinese science Bulletin 1997年第14期42卷 1149-1151页

作者： WU Qiguanginstitute of systems science, chinese academy of sciences, beijing 100080, china institute of systems science Chinese Academy of Sciences Beijing China

THROUGHOUT this note, the following notations are used: For a matrix A, A>0 means thatA is positive definite symmetric; R （A）, A′and A- stand for the column space, transposeand any g-inverse of A respectively; PA = A （A′A）- A′and PA = Ik - PA, where Ik is theidentity matrix of order k that is the number of rows in A. Rm×n is the totality of m×n realmatrices.

关键词： seemingly unrelated regression equations (SURE) model uniformly minimum risk unbiased (UMRU) estimator uniform covariance structure serial covariance structure.

A simple proof of the formal duality of the Kerdock and Preparata codes

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chinese science Bulletin 2000年第14期45卷 1279-1282页

作者： WAN Zhexianinstitute of systems science, chinese academy of sciences, beijing 100080, china institute of systems science Chinese Academy of Sciences Beijing China

The nonlinearity of the Z2-Kerdock code Km+1, where m is an odd integer ≥3, is not at all obvious. By regarding Km+1 as the binary image of the Z4-Kerdock code .,K(m) under the Gray map[1], a simple proof can be achieved (cf. Theorems 8.7 and 8.9 of [2]). Similarly, the formal duality of the Z2-Kerdock code Km+1 and the Z2-Preparata code Pm+1 is even more not at all obvious. A simple proof is given in the present note, by regarding Km+1 as the binary image of .K (m) and using the duality of .K(m) and the Z4-Preparata code . (m) established in [1].

关键词： 4-code. Kerdock code Preparata code formal duality.

Economical cascadic multigrid method (ECMG)

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science china mathematics 2007年第12期50卷 1765-1780页

作者： Zhong-ci SHI~1 Xue-jun XU~(1+) Yun-qing HUANG~2 ~1 LSEC,institute of Computational mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china ~2 Hunan Key Laboratory for Computation and Simulation in science and Engineering,institute for Computational and applied mathematics,Xiangtan University,Xiangtan 411105,china LSEC Institute of Computational Mathematics Academy of Mathematics systems science Chinese Academy of Sciences Beijing 100080 China Hunan Key Laboratory for Computation Simulation in science Engineering Institute for Computational applied mathematics Xiangtan University Xiangtan 411105 China

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

关键词： economical cascadic multigrid method (ECMG), cascadic multigrid method (CMG)