Title

Iterative Implementation Of The Adaptive Regularization Yields Optimality

Keywords

Ill-posed problems; Non-stationary iterated adaptive regularization; Optimality.

Abstract

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.

Publication Date

4-1-2005

Publication Title

Science in China, Series A: Mathematics

Volume

48

Issue

4

Number of Pages

485-492

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1360/03ys0326

Socpus ID

17644396355 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/17644396355

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