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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 17, Issue 2 (Jun 2007)


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

Dorota Krawczyk-Stańdo
  • Center of Mathematics and Physics, Technical University of Łódź, ul. Al. Politechniki 11, 90-924 Łódź, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Marek Rudnicki
  • Institute of Computer Science, Technical University of Łódź, ul. Wólczańska 215, 90-924 Łódź, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2007-07-17 | DOI: https://doi.org/10.2478/v10006-007-0014-3

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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About the article

Published Online: 2007-07-17

Published in Print: 2007-06-01

Citation Information: International Journal of Applied Mathematics and Computer Science, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/v10006-007-0014-3.

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