<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

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

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

International Journal of Applied Mathematics and Computer Science

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

Published Online: Jul 17, 2007

Page range: 157 - 164

DOI: https://doi.org/10.2478/v10006-007-0014-3

Keywords
ill-posed problems, Tikhonov regularization, regularization parameter, L-curve, U-curve

This content is open access.

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

Published Online: Jul 17, 2007

Page range: 157 - 164

DOI: https://doi.org/10.2478/v10006-007-0014-3

Keywordsill-posed problems, Tikhonov regularization, regularization parameter, L-curve, U-curve

This content is open access.

Keywords
ill-posed problems, Tikhonov regularization, regularization parameter, L-curve, U-curve