Tikhonov regularization based on generalized Krylov subspace methods

Lothar Reichel; Fiorella Sgallari; Qiang Ye

doi:10.1016/j.apnum.2010.10.002

Tikhonov regularization based on generalized Krylov subspace methods

Lothar Reichel, Fiorella Sgallari, Qiang Ye

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

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.

Original language	English
Pages (from-to)	1215-1228
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	62
Issue number	9
DOIs	https://doi.org/10.1016/j.apnum.2010.10.002
State	Published - Sep 2012

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (L. Reichel), [email protected] (F. Sgallari), [email protected] (Q. Ye). 1 Work partially supported by PRIN, grant 20083KLJEZ. 2 Supported in part by NSF under grant DMS-0915062.

Keywords

Ill-posed problem
Multiparameter regularization
Regularization operator
Tikhonov regularization

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2010.10.002

Cite this

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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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author = "Lothar Reichel and Fiorella Sgallari and Qiang Ye",

note = "Funding Information: E-mail addresses: [email protected] (L. Reichel), [email protected] (F. Sgallari), [email protected] (Q. Ye). 1 Work partially supported by PRIN, grant 20083KLJEZ. 2 Supported in part by NSF under grant DMS-0915062.",

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AU - Sgallari, Fiorella

AU - Ye, Qiang

N1 - Funding Information: E-mail addresses: [email protected] (L. Reichel), [email protected] (F. Sgallari), [email protected] (Q. Ye). 1 Work partially supported by PRIN, grant 20083KLJEZ. 2 Supported in part by NSF under grant DMS-0915062.

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N2 - 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.

AB - 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.

KW - Ill-posed problem

KW - Multiparameter regularization

KW - Regularization operator

KW - Tikhonov regularization

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 9

ER -

Tikhonov regularization based on generalized Krylov subspace methods

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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