Adaptive Algorithms of Nonlinear Approximation with Finite Terms  

作　　者：Wen Bin WEI Yue Sheng XU Pei Xin YE 

机构地区：[1]Department 4, Air Force Radar Academy, Wuhan 430019, P. R. China [2]Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, P. R. China [3]Department of Mathematics, Nankai University, Tianjin 300000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第9期1663-1672,共10页数学学报（英文版）

基　　金：the foundation under the program of"One Hundred Outstanding Young Chinese Scientists"of the Chinese Academy of Sciences;the Graduate Innovation Foundation of the Chinese Academy of Sciences

摘　　要：This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm Gm^P（., Ψ）. This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another Mgorithm introduced by Birge and Massart.This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm Gm^P（., Ψ）. This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another Mgorithm introduced by Birge and Massart.

关 键 词：nonlinear approximation DICTIONARY Haar system adaptive algorithm near best approximation 

分 类 号：O15[理学—数学]