A wavelet operational method for solving fractional partial differential equations numerically

Fractional calculus is an extension of derivatives and integrals to non-integer orders, and a partial differential equation involving the fractional calculus operators is called the fractional PDE. They have many applications in science and engineering. However not only the analytical solution existed for a limited number of cases, but also the numerical methods are very complicated and difficult. In this paper, we newly establish the simulation method based on the operational matrices of the orthogonal functions. We formulate the operational matrix of integration in a unified framework. By using the operational matrix of integration, we propose a new numerical method for linear fractional partial differential equation solving. In the method, we (1) use the Haar wavelet; (2) establish a Lyapunov-type matrix equation; and (3) obtain the algebraic equations suitable for computer programming. Two examples are given to demonstrate the simplicity, clarity and powerfulness of the new method.     

Error estimates in S P for cubature formulas exact for haar polynomials in the two-dimensional case

On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for $ \left\| {\delta _N (f)} \right\|_{S_p^* } On the spaces S _p , an upper estimate is found for the norm of the error functional δ _N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for with the number of nodes N ∼ 2 ^d , where d → ∞. For N ∼ 2 ^d with d → ∞, it is shown that the norm of δ _N for the formulas under study has the best convergence rate, which is equal to N ^−1/p . Original Russian Text ? K.A. Kirillov, M.V. Noskov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 1, pp. 3–13.     

Universal optimality of digital nets and lattice designs

This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are...     

应用Haar小波和算子矩阵求定积分的近似值

将Haar小波与算子矩阵有效结合,对被积函数进行恰当的离散,把一些不易求得原函数的定积分问题转化成计算常数矩阵的乘积。由于矩阵的乘积可以直接用MATLB来实现,从而使得计算简便,最后给出数值算例验证了方法的有效性。     

基于Haar小波的虹膜特征提取算法

虹膜特征提取算法的优劣决定了虹膜识别系统的性能,经典小波变换算法在特征提取上存在不足,提出一种利用二维Haar小波提取虹膜特征的算法。算法在虹膜预处理的基础上,利用2D Haar小波对虹膜特征提取区域分解,对第三层小波分解高频系数编码生成375bits虹膜编码,利用相似度作为特征匹配关系。在中国科学院虹膜数据库[CASIA(1.0)]上的实验结果表明,算法在认证模式(Verification)与识别模式(Identification)下,性能均优于Boles的算法和Wildes的算法,仅次于Daugman的算法;但本算法虹膜码长度仅为Daugman的1/5,更节省储存空间,正确识别率为99.16%,等错率达到0.54%。     

基于Haar小波特征的恒星光谱物理参量自动估计

恒星大气物理参数的自动测量是大型巡天计划中海量光谱数据自动处理中的一个重要内容。首先使用多尺度Harr小波对恒星光谱数据进行特征分解,然后选用相应的小波系数作为光谱的特征向量,最后采用非参数回归算法对光谱的物理参数进行估计。研究表明,只需对光谱进行四层小波分解, 并选择第四层小波系数作为光谱的特征向量,即可获得重力加速度和表面有效温度的较好估计。对于化学丰度的估计,选择第一层小波系数作为光谱特征向量可取得较好效果。选用文献相关研究中常用的恒星大气模拟模型合成光谱库ELODIE中光谱数据测试了该方法的有效性。结果表明,基于Harr小波分解的光谱特征提取方法对恒星表面温度、表面重力和化学丰度等物理参数的估计具有较高的精度和鲁棒性。     

基于Gamma和AdaBoost的人脸检测系统设计

为了有效地实现人脸的检测效果,文章在AdaBoost算法基础上提出一个改进的人脸检测算法．为了有效地消除光照和成像对人脸的影响,该算法将Canny修剪算法和伽马矫正算法进行结合,有效地消除光照和成像设备对人脸的影响．并利用VisualC＋＋和OpenCV等开发工具设计了一个人脸检测系统．本系统采用20×20的人脸图像和背景图像各1000张训练了一个7层的级联分类器,每一层构成的强分类器由一组基于Haar特征的弱分类器构成．该系统通过自选137幅包含人脸和背景的图片对系统进行测试,获得94．72％的正确检测率以及26．42％的误检率．     

Transformation of Some Mixed Approximation Problems by Optimization Methods

The present paper considers the approximation of a function in the L 2 -norm by functions in a Haar space subject to a constraint set defined by the sup norm. This problem is examined from developments of the Karush-Kuhn-Tucker theorem for semi-infinite programming as well as from the multiobjective optimization approach. An extreme feasible set is characterized with the help of a version of the Chebyshev alternation theorem.     

Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method

In this paper, we present a computational method for solving 2D and 3D Poisson equations and biharmonic equations which based on the use of Haar wavelets. The highest derivative appearing in the differential equation is expanded into the Haar series, this approximation is integrated while the boundary conditions are incorporated by using integration constants. In 2D the first transform the spectral coefficients into the nodal variable values and then use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solutions to four test problems are investigated.     

基于Haar小波变换和分块DCT的人耳识别

提出一种新的对人耳图像进行降维的方法。先对人耳图像进行二维的离散小波分解,然后再对小波分解后得到的低频信息施行分块离散余弦变换,进而获得图像的特征向量。实验证明,该方法与模式识别领域中广泛应用的PCA-LDA方法相比,在识别率大体相当的前提下,具有计算量小、降维速度快的优点,是对人耳图像进行特征提取的一种有效的手段。