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International Journal of Applied Mathematics and Computer Science

The Journal of University of Zielona Gora and Lubuskie Scientific Society

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Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve

Dorota Krawczyk-Stańdo1 / Marek Rudnicki1

Center of Mathematics and Physics, Technical University of Łódź, ul. Al. Politechniki 11, 90-924 Łódź, Poland1

Institute of Computer Science, Technical University of Łódź, ul. Wólczańska 215, 90-924 Łódź, Poland2

This content is open access.

Citation Information: International Journal of Applied Mathematics and Computer Science. Volume 17, Issue 2, Pages 157–164, ISSN (Print) 1641-876X, DOI: 10.2478/v10006-007-0014-3, July 2007

Publication History

Published Online:
2007-07-17

Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve

To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.

Keywords: ill-posed problems; Tikhonov regularization; regularization parameter; L-curve; U-curve

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