Iterative implementation of the adaptive regularization yields optimality  

作　　者：MA Qinghua & WANG Yanfei Department of Information Sciences, College of Arts and Science of Beijing Union University, Beijing 100038, China National Key Laboratory on Remote Sensing Science, Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing 100101, China Department of Mathematics, University of Central Florida, P. O. Box 161364, Orlando, FL 32816-1364, USA 

出　　处：《Science China Mathematics》2005年第4期485-492,共8页中国科学：数学（英文版）

基　　金：This work was supported by the research program of College of Arts and Science of Beijing Union University and SRF for ROCS,SEM.

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 itis adaptive, i.e. it eliminates the small eigenvalues of theadjoint 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.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.

关 键 词：ILL-POSED problems  NON-STATIONARY ITERATED adaptive regularization  optimality. 

分 类 号：O224[理学—运筹学与控制论]