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...
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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 the corresponding directions.
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-...
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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.
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 app...
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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.
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 ty...
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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 Ho...
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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 numericallinearalgebra 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/).
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...
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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.
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 approxima...
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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.
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 ...
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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.
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 o...
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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 numericalmethods 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 numericalmethods 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.
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 nonlinearitie...
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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.
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