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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)

IMPLICIT—EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

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Journal of systems science & Complexity 2003年第1期16卷 101-103页

作者： CHENWei DepartmentofEconomics ShandongUniversityJinan250100AcademyofMathematicsandSystemsScienceChineseAca

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole *** electric potential equation is discretized by the finite element *** electron and hole density equations are treated by implicit-explicit multistep finite element *** optimal L^2-norm error estimates are derived.

关键词：半导体有限元方法泊松方程非线性抛物方程电位电荷密度

On ultraproducts of operator algebras

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science china mathematics 2005年第9期 134-145页

作者： LI Weihua Institute of mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china

Some basic questions on ultraproducts of C-algebras and von Neumann al- gebras,including the relation to K-theory of C-algebras are *** specifically, we prove that under certain conditions,the K-groups of ultraproduct of C-algebras are iso- morphic to the ultraproduct of respective K-groups of *** also show that the ultraproducts of factors of type Ⅱare prime,*** isomorphic to any non-trivial tensor product.

关键词： von Neumann algebras C-algebras ultraproducts K-group double commutants

Approximation of dense-n/2-subgraph and table compression problems

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science china mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2 & DU Dongle~3 1. College of Applied sciences,beijing University of Technology,beijing 100022,china 2. Institute of Applied mathematics,academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china 3. Faculty of Administration,University of New Brunswick,P.O.Box 4400,Fredericton,NB E3B 5A3,Canada College of Applied sciences Beijing University of Technology Beijing 100022 China Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table *** on SDP relaxation and advanced rounding techniques,we first propose 0. 5982 and 0. 5970-approximation algorithms respec- tively for the dense-n/2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0. 6243 and 0. 6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP *** results for TCP beat the 0. 5 bound of a simple greedy algorithm on this problem,and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2-subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio

EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

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Journal of systems science & Complexity 2007年第3期20卷 437-443页

作者： Weiwei HU Houbao XU Jingyuan YU Guangtian ZHU beijing Institute of Information and Control Beijing 100037 China. Department of mathematics Beijing Institute of Technology Beijing 100081 China. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100080 China.

The exponential stability of a multi-state device is discussed in this paper. We present that the Co-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue O.

关键词： C0-semigroup exponential stability irreducibility quasi-compact.

On the use of simplex methods in constructing quadratic models

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science china mathematics 2007年第7期50卷 913-924页

作者： Qing-hua ZHOU 1 College of mathematics and Computer,Hebei University,Baoding 071002,china 2 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 100080,china College of mathematics Computer Hebei University Baoding 071002 China State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics systems science Chinese Academy of Sciences Beijing 100080 China

In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.

关键词： unconstrained optimization trust region method quadratic model Lagrange function simplex methods direct methods 90C56

On conformal measures for infinitely renormalizable quadratic polynomials

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science china mathematics 2005年第10期48卷 1411-1420页

作者： HUANG Zhiyong~1 JIANG Yunping~(2,3) & WANG Yuefei~3 1. School of Information,Renmin University of china,beijing 100872,china 2. Department of mathematics,Queens College,City University of New York,NY 11367,USA Department of mathematics,Graduate School,City University of New York,New York,NY 10016,USA 3. academy of mathematics and systems science,chinese academy of sciences,beijing 100080,china 1. School of Information Renmin University of China 100872 Beijing China 2. Department of mathematics Queens College City University of New York 11367 NY USA 3. Department of mathematics Graduate School City University of New York 10016 New York NY USA 4. academy of mathematics and systems science Chinese Academy of Sciences 100080 Beijing China

We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t... 详细信息

关键词： Julia set, conformal measure, three-dimensional puzzle, infinitely renormalizable quadratic polynomial.

ON-LINE PREEMPTIVE SCHEDULING ON UNIFORM MACHINES

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Journal of systems science & Complexity 2001年第4期14卷 373-377页

作者： ZHANG Yuzhong (Institute of Operations Research, Qufu Normal University, Qufu 273165, china) WANG Shouyang (Institute of systems science, academy of mathematics and systems science, chinese academy of sciences, beijing 100080, china) Bo Chen (Warwick Busi 曲阜师范大学山东曲阜 273165 中科院系统科学所北京 100080 University of Warwick 英国 CV4 7AL 镇江水运学院江苏镇江 212003

We address the problem of preemptively schedule on-line jobs on arbitrary m uniformly related machines with the objective of minimizing the schedule length. We provide the first on-line algorithm for this general problem, and show that the algorithm has a competitive ratio of 1 ± σ, where a (m - 1)s1/(si +…+ sm), S1 S2 Sm being the speeds of the m machines.

关键词： On-line scheduling uniformly related machines preemption competitive ratio.

A GENERAL APPROACH BASED ON AUTOCORRELATION TO DETERMINE INPUT VARIABLES OF NEURAL NETWORKS FOR TIME SERIES FORECASTING

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Journal of systems science & Complexity 2004年第3期17卷 297-305页

作者： HUANGWei NAKAMORIYoshiteru WANGShouyang SchoolofKnowledgescience JapanAdvancedInstituteofScienceandTechnologyAsahidai1-1TatsunokuchiIshikawa923-1292Japan Instituteofsystemsscience AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China

Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to finance, time series forecasting is perhaps one of the most challenging issues. Considering the features of neural networks, we propose a general approach called Autocorrelation Criterion (AC) to determine the inputs variables for a neural network. The purpose is to seek optimal lag periods, which are more predictive and less correlated. AC is a data-driven approach in that there is no prior assumptiona bout the models for time series under study. So it has extensive applications and avoids a lengthy experimentation and tinkering in input selection. We apply the approach to the determination of input variables for foreign exchange rate forecasting and conductcomparisons between AC and information-based in-sample model selection criterion. The experiment results show that AC outperforms information-based in-sample model selection criterion.

关键词： input variables foreign exchange rate neural networks time seriesforecasting