Greedy Algorithm in m-Term Approximation for Periodic Besov Class with Mixed Smoothness  

作　　者：宋占杰 叶培新 

机构地区：[1]School of Sciences, Tianjin University [2]School of Electronic Information Engineering, Tianjin University [3]School of Mathematical Sciences and LPMC, Nankai University

出　　处：《Transactions of Tianjin University》2009年第1期75-78,共4页天津大学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (No. 60872161, 10501026, 60675010 and 10626029);Natural Science Foundation of Tianjin (No. 08JCYBJC09600);China Postdoctoral Science Foundation ( No. 20070420708).

摘　　要：Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m -term approximation with regard to tensor product wavelet-type basis is pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m-term approximation with regard to tensor product wavelet-type basis is proposed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the Lq norm. Moreover, it depends only on the expansion of functionf by tensor product wavelet-type basis, but neither on q nor on any special features of f

关 键 词：greedy algorithm m -term approximation Besov space mixed smoothness 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]