A modified Tikhonov regularization for linear operator equations

    Authors

    G. S. Li;Z. Nashed

    Comments

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    Abbreviated Journal Title

    Numer. Funct. Anal. Optim.

    Keywords

    convergence and asymptotic order of the regularized solutions; error; analysis; first kind operator equation; ill-posed problem; modified; Tikhonov regularization; ILL-POSED PROBLEMS; PARAMETER; CHOICE; ERROR; Mathematics, Applied

    Abstract

    We construct with the aid of regularizing filters a new class of improved regularization methods, called modified Tikhonov regularization (MTR), for solving ill-posed linear operator equations. Regularizing properties and asymptotic order of the regularized solutions are analyzed in the presence of noisy data and perturbation error in the operator. With some accurate estimates in the solution errors, optimal convergence order of the regularized solutions is obtained by a priori choice of the regularization parameter. Furthermore, numerical results are given for several ill-posed integral equations, which not only roughly coincide with the theoretical results but also show that MTR can be more accurate than ordinary Tikhonov regularization (OTR).

    Journal Title

    Numerical Functional Analysis and Optimization

    Volume

    26

    Issue/Number

    4-5

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    543

    Last Page

    563

    WOS Identifier

    WOS:000232803000005

    ISSN

    0163-0563

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