〈I〉型三角剖分下非张量积连续小波基的构造

多维非张量积小波是近年小波研究领域中的热点问题之一 ,它们与多维张量积小波相比具有更多的优势 .关于高维张量积、非张量积小波 ,目前已有一些很好的工作 (见文[2 ] [3 ] [4 ] ) ,但关于样条小波 ,还有许多问题有待于研究 .本文针对〈I〉型三角剖分下的二维线性元空间 ,讨论其具有紧支集和对称性的半正交样条小波基 .给定 x1 x2 平面上的〈I〉型三角剖分 (图 1 ( a)所示 ) ,记 j=( j1 ,j2 ) ,| j| =j1 + j2 ,πm= { 0≤ |j|≤ mCj1j2 xj11 xj22 ,Cj1,j2 是任意实数 }为次数不超过 m的代数多项式全体 .引入剖分尺度为 1的线性元空间 V0…     

Ⅱ型三角剖分上二次双周期样条

本文用B-网方法确定了△_(nm)~((2))剖分上二次双周期样条函数空间的维数,给出了插值条件的几种提法,证明了解的存在唯一性.     

Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner–Fox–Schmit rectangular element and the product two‐point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. The preconditioners are implemented by optimal algorithms, and they are used to accelerate convergence of the preconditioned conjugate gradient method. Numerical results are presented demonstrating efficiency of the preconditioners. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

On wavelets interpolated from a pair of wavelet sets

We show that any wavelet, with the support of its Fourier transform small enough, can be interpolated from a pair of wavelet sets. In particular, the support of the Fourier transform of such wavelets must contain a wavelet set, answering a special case of an open problem of Larson. The interpolation procedure, which was introduced by X. Dai and D. Larson, allows us also to prove the extension property.

     

基于Gabor小波纹理特征的目标识别新方法

给出了一种基于Gabor小波纹理特征的目标识别新方法．主要是利用Gabor小波设计了一种多通道小波滤波器。对图像目标直接进行小波变换，用Gabor小波变换系数的模的平均值和其标准方差来表示抽取的图像目标的特征，把获得的小波特征归一化后输入到改进的BP神经网络分类器进行分类识别．最后。进行了一系列的仿真实验，结果表明，这种特征提取方法能有效提取图像目标纹理特征，并且对噪音和形状的变化具有鲁棒性．在应用于目标识别时，神经网络的训练时间减少到lOmin，识别率达到94％．     

Oracle Inequalities for Efromovich–Pinsker Blockwise Estimates

Oracle inequality is a relatively new statistical tool for the analysis of nonparametric adaptive estimates. Oracle is a good pseudo-estimate that is based on both data and an underlying estimated curve. An oracle inequality shows how well an adaptive estimator mimics the oracle for a particular underlying curve. The most advanced oracle inequalities have been recently obtained by Cavalier and Tsybakov (2001) for Stein type blockwise estimates used in filtering a signal from a stationary white Gaussian process. The authors also conjecture that a similar result can be obtained for Efromovich–Pinsker (EP) type blockwise estimators where their approach, based on Stein's formula for risk calculation, does not work. This article proves the conjecture and extends it upon more general models which include not stationary and dependent processes. Other possible extensions, a discussion of practical implications and a numerical study are also presented.     

Wavelets and adaptive grids for the discontinuous Galerkin method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.     

一类常微分方程组的紧支撑样条小波方法探讨

应用三次紧支撑样条小波插值函数得到了求一类常微分方程组数值解的隐式公式,并求得到其局部截断误差为O(-h5).在此基础上给出1个显式校正求解公式,并讨论得到其局部截断误差为O(-h4).     

On interpolatory divergence-free wavelets

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct compactly supported divergence-free interpolatory wavelets.