文献类型：期刊文献

英文题名：Iterative implementation of the adaptive regularization yields optimality

作者：Ma Q.[1];Wang Y.[2,3]

第一作者：马青华

通讯作者：Ma, QH[1]

机构：[1]Beijing Union Univ, Coll Arts & Sci, Dept Informat Sci, Beijing 100038, Peoples R China;[2]Chinese Acad Sci, Inst Remote Sensing Applicat, Natl Key Lab Remote Sensing Sci, Beijing 100101, Peoples R China;[3]Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

第一机构：北京联合大学应用文理学院

通讯机构：[1]corresponding author), Beijing Union Univ, Coll Arts & Sci, Dept Informat Sci, Beijing 100038, Peoples R China.|[114172]北京联合大学应用文理学院;[11417]北京联合大学;

年份：2005

卷号：48

期号：4

起止页码：485-492

外文期刊名：SCIENCE IN CHINA SERIES A-MATHEMATICS

收录：;EI(收录号：2005189082153);Scopus(收录号：2-s2.0-17644396355);WOS:【SCI-EXPANDED(收录号:WOS:000229229700005)】；

基金：Acknowledgements We would like to express our sincere thanks to the referees for their valuable comments. Especially, we appreciate the referee’s suggestions for choosing the new dominant function in sec. 2, which leads to the present improved version of the manuscript. This work was supported by the research program of College of Arts and Science of Beijing Union University and SRF for ROCS, SEM.

语种：英文

外文关键词：ill-posed problems; non-stationary iterated adaptive regularization; optimality

摘要：The adaptive regularization method is first proposed by Ryzhikov et al. for the deconvolution in elimination of multiples. This method is stronger than the Tikhonov regularization in the sense that it is adaptive, i.e. it eliminates the small eigenvalues of the adjoint operator when it is nearly singular. We will show in this paper that the adaptive regularization can be implemented iterately. Some properties of the proposed non-stationary iterated adaptive regularization method are analyzed. The rate of convergence for inexact data is proved. Therefore the iterative implementation of the adaptive regularization can yield optimality.