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Preservation of linear Constraints in Approximation of Tensors

numerical Mathematics(theory,methods and applications) 2009年第4期2卷 421-426页

作者： Eugene Tyrtyshnikov Institute of Numerical Mathematics of Russian Academy of Sciences

For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for t... 详细信息

关键词： Multi-index arrays tensors linear constraints low rank approximation canonicaltensor decomposition multilevel matrices.

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Observer-based resilient L₂-L_∞ control for singular time-delay systems

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IET CONTROL theory AND applications 2009年第10期3卷 1351-1362页

作者： Li, L. Jia, Y. Beihang Univ Dept Syst & Control Beijing 100191 Peoples R China

The problem of non-fragile (or resilient) L-2-L-infinity control for a class of singular systems with time-varying delay is considered via observer-based state feedback control. The objective is to design an observer-based feedback controller with additive gain variations such that, for all admissible observer and controller gain variations, the closed-loop system is regular, impulse free and stable with a prescribed L-2-L-infinity performance index satisfied. In terms of linear matrix inequalities, a new delay-dependent stability criterion is derived. Based on the obtained criterion, the non-fragile observer and controller design method is proposed. numerical example and simulation results are included to show the effectiveness of the proposed results.

关键词： performance index feedback controller design nonfragile L2-L∞ control time-varying systems Time-varying control systems stability control system synthesis Stability in control theory Control system analysis and synthesis methods state feedback state feedback control closed loop systems algebra resilient L2-L∞ control delay-dependent stability criterion time-varying delay linear matrix inequalities observer L2-L∞ performance index closed-loop system observers additive gain variations Simulation, modelling and identification Distributed parameter control systems delay systems singular time-delay systems

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On Superlinear PCG methods for FDM Discretizations of Convection-Diffusion Equations

On Superlinear PCG Methods for FDM Discretizations of Convec...

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4th International conference on numerical Analysis and applications

作者： Karatson, Janos Kurics, Tamas ELTE Univ Dept Appl Anal & Computat Math H-1117 Budapest Hungary

ISBN: (纸本)9783642004636

The numerical solution of linear convection-diffusion equations is considered. Finite difference discretization leads to an algebraic system solved by a suitable preconditioned CC method, where the preconditioning approach is based on equivalent operators. Our goal is to study the superlinear convergence of the preconditioned CC iteration and to find mesh independent behaviour on a model problem. This is an analogue of previous results where FEM discretization was used.

关键词： algebra

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Non-solvable groups are not in FO+MOD+M - AJ2[REG]

Non-solvable groups are not in FO+MOD+M - AJ2[REG]

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3rd International conference on Language and Automata theory and applications, LATA 2009

作者： Behle, Christoph Krebs, Andreas Reifferscheid, Stephanie WSI - University of Tübingen Sand 13 72076 Tübingen Germany

ISBN: (纸本)9783642009815

Motivated by the open question whether TC0 = NC1 we consider the case of linear size TC0. We use the connections between circuits, logic, and algebra, in particular the characterization of TC 0 in terms of finitely typed monoids. Applying algebraic methods we show that the word problem for finite non-solvable groups cannot be described by a FO+MOD+MAJ[REG] formula using only two variables. This implies a separation result of FO[REG]-uniform linear TC0 from linear NC1. © Springer-Verlag Berlin Heidelberg 2009.

关键词： algebra

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Special Issue for Image Processing and numerical linear algebra

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numerical Mathematics(theory,methods and applications) 2009年第4期 5-6页

作者： Michael K.Ng Eugene Tyrtyshnikov Department of Mathematics and Centre for Mathematical Imaging and Vision Hong Kong Baptist University Institute of Numerical Mathematics of the Russian Academy of Sciences and Institute for Computational Mathematics Hong Kong Baptist University

The Third International conference on Scientific Computing and Partial Differential Equations(SCPDE) was held from December 8 to December 12,2008 at Hong Kong Baptist *** was a sequel to similar conferences held in Hong Kong(2002 and 2005). The conference aims to promote research interests in scientific *** SCPDE 2008,two workshops on image processing and numerical linear algebra are organized to review recent scientific developments and explore exciting new directions in mathematical modeling and computational methods in these two *** are twenty one invited speakers in these two workshops(http://***/SCPDE08/).

关键词： Special Issue for Image Processing and numerical linear algebra

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Stability Criterions for Switched linear Systems Based on Matrix Measure

Stability Criterions for Switched Linear Systems Based on Ma...

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4th IEEE conference on Industrial Electronics and applications

作者： Zou, Hongbo Li, Han Xu, Ouguan Hangzhou Dianzi Univ Inst Informat & Control Hangzhou 310018 Zhejiang Peoples R China China Bldg Tech Grp Co Ltd Inst Design 3 Beijing 100013 Peoples R China Zhejiang Univ Technol Hangzhou 310024 Peoples R China

ISBN: (纸本)9781424427994

The problem of stability analysis for a class of switched linear systems is studied in this paper based on the theory of matrix measure. The matrix measures of all subsystems are used to determine the stability of the switched linear systems. Based on this, sufficient conditions are reached, which can be used to determine the stability or instability of switched linear systems under arbitrary switching law. If a switching sequence satisfies some conditions, a theorem in this paper can be used to verify if it can stabilize the systems. The obtained conditions are simpler than the reported methods such as multi-Lyapunov functions and hence are easier to check. numerical examples are used to demonstrate these conditions.

关键词： Hybrid systems Switched Systems Matrix Measure

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A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

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numerical Mathematics(theory,methods and applications) 2009年第4期2卷 377-402页

作者： Zheng-Jian Bai Michael K. Ng Liqun Qi School of Mathematical Sciences Xiamen University Xiamen 361005 China Centre for Mathematical Imaging and Vision and Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong Department of Applied Mathematics The Hong Kong Polytechnic University Hung Horn Hong Kong

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex *** find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex *** a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence *** also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.

关键词： Coordinate descent global convergence linear convergence rate

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A High-Quality Preconditioning Technique for Multi-Length-Scale Symmetric Positive Definite linear Systems

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numerical Mathematics(theory,methods and applications) 2009年第4期2卷 469-484页

作者： Ichitaro Yamazaki Zhaojun Bai Wenbin Chen Richard Scalettar Department of Computer Science University of California Davis CA 95616 USA School of Mathematical Sciences Fudan University Shanghai 200433 China Department of Physics University of California Davis CA95616 USA

We study preconditioning techniques used in conjunction with the conjugate gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale systems. In this paper, we propose a hybrid incomplete Cholesky （HIC） preconditioner and demonstrate its adaptivity to the multi-length-scale systems. In addition, we propose an extension of the compressed sparse column with row access （CSCR） sparse matrix storage format to efficiently accommodate the data access pattem to compute the HIC preconditioner. We show that for moderately correlated materials, the HIC preconditioner achieves the optimal linear scaling of the simulation. The development of a linear-scaling preconditioner for strongly correlated materials remains an open topic.

关键词： Preconditioning multi-length-scale incomplete Cholesky factorization quantum MonteCarlo simulation.

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Computing quadratic approximations for the isochrons of oscillators: A general theory and advanced numerical methods

Computing quadratic approximations for the isochrons of osci...

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2009 IEEE/ACM International conference on Computer-Aided Design, ICCAD 2009

作者： Şuvak, Önder Demir, Alper Koç University Istanbul Turkey

ISBN: (纸本)9781605588001

We first review the notion of isochrons for oscillators, which has been developed and heavily utilized in mathematical biology in studying biological oscillations. Isochrons were instrumental in introducing a notion of generalized phase for an oscillation and form the basis for oscillator perturbation analysis formulations. Calculating the isochrons of an oscillator is a very difficult task. Except for some very simple planar oscillators, isochrons can not be calculated analytically and one has to resort to numerical techniques. Previously proposed numerical methods for computing isochrons can be regarded as brute-force, which become totally impractical for non-planar oscillators with dimension more than two. In this paper, we present a precise and carefully developed theory and advanced numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the theory and the numerical methods needed for computing only linear approximations for isochrons. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple case, and allude to several applications among many where quadratic approximations of isochrons will be of use. Copyright 2009 ACM.

关键词： numerical methods

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Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions

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NONlinear ANALYSIS-theory methods & applications 2009年第5期70卷 1803-1812页

作者： Montagner, V. F. Oliveira, R. C. L. F. Calliero, T. R. Borges, R. A. Peres, P. L. D. Prieur, C. Univ Toulouse 2 CNRS LAAS F-31077 Toulouse 4 France CT Alegrete UNIPAMPA GEPOC UFSM BR-97546550 Alegrete RS Brazil Univ Estadual Campinas Sch Elect & Comp Engn BR-13081970 Campinas SP Brazil

This paper provides finite-dimensional convex conditions to construct homogeneous polynormally parameter-dependent Lur'e functions which ensure the stability of nonlinear systems with state-dependent nonlinearities lying in general sectors and which are affected by uncertain parameters belonging to the unit simplex. The proposed conditions are written as linear matrix inequalities parametrized in terms of the degree g of the parameter-dependent solution and in terms of the relaxation level d of the inequality constraints, based on the algebraic properties of positive matrix polynomials with parameters in the unit simplex. As g and d increase, progressively less conservative solutions are obtained. The results in the paper include as special cases existing conditions for robust stability and for absolute stability analysis. A convex solution suitable for the design of robust nonlinear state feedback stabilizing controllers is also provided. numerical examples illustrate the efficiency of the proposed conditions. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： NONlinear systems MATRIX inequalities STABILITY (Mechanics) POLYNOMIALS algebra MATHEMATICAL analysis INEQUALITIES (Mathematics)

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