Iterative implementation of the adaptive regularization yields optimality

    Authors

    Q. H. Ma;Y. F. Wang

    Comments

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    Abbreviated Journal Title

    Sci. China Ser. A-Math.

    Keywords

    ill-posed problems; non-stationary iterated adaptive regularization; optimality; ILL-POSED PROBLEMS; TIKHONOV REGULARIZATION; Mathematics, Applied; Mathematics

    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.

    Journal Title

    Science in China Series a-Mathematics

    Volume

    48

    Issue/Number

    4

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    485

    Last Page

    492

    WOS Identifier

    WOS:000229229700005

    ISSN

    1006-9283

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