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Tree wavelet approximations with applications

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science china mathematics 2005年第5期48卷 680-702页

作者： XU Yuesheng & ZOU Qingsong Department of mathematics, Syracuse university, Syracuse, NY 13244, USA Institute of mathematics, Academy of mathematics and System sciences, Chinese Academy of sciences, Beijing 100080, china Department of scientific computing and computer science, zhongshan university, guangzhou 510275, china Department of mathematics Syracuse University Syracuse USA Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Department of scientific computing and computer science Zhongshan University Guangzhou China

We construct a tree wavelet approximation by using a constructive greedy scheme (CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.

关键词： greedy algorithms tree wavelet approximations Besov spaces.

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 510275, china) Dept. of mathematics Beijing Jiaotong Univ. Beijing 100044 China Inst. of mathematics Acad. of Math. and System Sci. Chinese Acad. of Sciences Beijing 100080 China Dept. of scientific computing Zhongshan Univ. 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

Congestion Control Protocol Based on Delay Parameters for Layered Multicast Communication

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Congestion Control Protocol Based on Delay Parameters for La...

MULTI-PARAMETER TIKHONOV REGULARIZATION FOR LINEAR ILL-POSED OPERATOR EQUATIONS

2006 10th International Conference on Communication Technology（ICCT 2006）

作者： BIAN Jing WANG Ze-qiang KE Hao-he Dept. of scientific computing & computer Application zhongshan university guangzhou Guangdong, 510275, china ZHANG Guang-zhao Dept. of Electronics & Communication Engineering zhongshan university guangzhou Guangdong, 510275, china

This paper focuses on the congestion control mechanism to be used in receiver-driven layered multicast. Since delay infers the transmission performances of jitter, bandwidth and throughput, it is necessary to concern delay properties in real-time multimedia transmission. In this paper, by analyzing the relationship between arrival delay intervals and network congestion, the congestion control parameter Intervalar i is obtained. By using delay parameters SR deg and SR det , the path’s available bandwidth can be estimated for the decision of layer join. By using the available bandwidth estimation results, Intervalar i and the packet-loss event Lost deg , a new layered multicast congestion control protocol BDP is proposed. The ns2 simulation results show that BDP can achieve scalability, stability, fast convergence and TCP- fairness.

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Journal of Computational mathematics 2008年第1期26卷 37-55页

作者： Zhongying Chen Yao Lu Yuesheng Xu Hongqi yang Department of scientific computing and computer applications Zhongshan University Guangzhou 510275 China Department of mathematics Syracuse University Syracuse NY 13244-1150 USA

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.

关键词： Ill-posed problems Tikhonov regularization Multi-parameter regularization

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