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Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2. and CHEN Qiuhui3(1. Department of mathematics, beijing Jiaotong University, beijing 100044, china 2. institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china 3. Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 5102.5, china) Department of mathematics Beijing Jiaotong University Beijing 100044 China. institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (institute of mathematics,{2., chinese academy of sciences, beijing 100080, china) institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method

ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 35-56页

作者： Lan Chieh Huang (ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,{2., china) ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the fully implicit Crank Nicholson (CN) schemes and three projection methods for approximate preservation of component-consistency under projection. Transformation from incompressible Navier-Stokes equations to differential algebraic equations CN schemes; Local errors of CN projection methods; Numerical boundary conditions.

关键词： differential algebraic equations discrete projection numerical boundary conditions

Transformations and non-degenerate maps

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Science china mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei institute of mathematics,{2., chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china 1. institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 100080 Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 225-238页

作者： Jian Li (LSEC, institute of Computational mathematics and Scientific/Engineering Computing,{2., chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.

关键词： Navier-Stokes equations Fourier-Legendre pseudospectral method error estimation

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

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Journal of Computational mathematics 2003年第6期21卷 733-746页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,{2. 100080, china) LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3/4) and O(h3/2. are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

关键词： Dual Mixed Method Unilateral Problem.

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

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Journal of Computational mathematics 2003年第5期21卷 613-624页

作者： Pu-yan Nie(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,{2., china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.

关键词： Composite-step like approaches Filter methods Equality constraints Sequen- tial quadratic programming(SQP) algorithms Normal component Tangential component Convergence.

SYMPLECTIC COMPUTATION OF HAMILTONIAN systemS (I)

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Journal of Computational mathematics 2002年第3期20卷 267-276页

作者： Yi-fa Tang(LSEC,ICMSEC,academy of mathematics and {2. sciences, chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

Presents information on a study which discussed a symplectic computation of hamiltonian systems. Terms of formal energy of mid-point rule; Analysis of the mathematical pendulum to test the convergence of the formal en... 详细信息

关键词： mid-point rule formal energy

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 2000年第3期18卷 313-324页

作者： Hua-zhong Tang (LSEC, institute of Computational mathematics and Scientific /Engineering Computing,{2., chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality