Elsevier

Applied Numerical Mathematics

Volume 62, Issue 9, September 2012, Pages 1215-1228
Applied Numerical Mathematics

Tikhonov regularization based on generalized Krylov subspace methods

https://doi.org/10.1016/j.apnum.2010.10.002Get rights and content

Abstract

We consider Tikhonov regularization of large linear discrete ill-posed problems with a regularization operator of general form and present an iterative scheme based on a generalized Krylov subspace method. This method simultaneously reduces both the matrix of the linear discrete ill-posed problem and the regularization operator. The reduced problem so obtained may be solved, e.g., with the aid of the singular value decomposition. Also, Tikhonov regularization with several regularization operators is discussed.

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      Citation Excerpt :

      In addition to the above classical approaches, quite a few studies based on other techniques have been proposed including preconditioning [15], as well as optimization tools [16,17]. For large-scale problems iterative or projection methods are proposed [18–23]. As well as, for other practical application of the Tikhonov’s regularization method see [24–26].

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    1

    Work partially supported by PRIN, grant 20083KLJEZ.

    2

    Supported in part by NSF under grant DMS-0915062.

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