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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)

Issues

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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  • Hansen P.C. (1992): Analysis of discrete ill-posed problems by means of the L-curve.— SIAM Rev., Vol. 34, No. 4, pp. 561-580.CrossrefGoogle Scholar

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  • Hansen P.C. (1993): Regularization Tools, a Matlab package for analysis and solution of discrete ill-posed problems. — Report UNIC-92-03Google Scholar

  • Krawczyk-Stańdo D. and Rudnicki M. (2005): Regularized synthesis of the magnetic field using the L-curve approach. — Int. J. Appl. Electromagnet. Mech., Vol. 22, No. 3-4, pp. 233-242.Google Scholar

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  • Stańdo J., Korotow S., Rudnicki M., Krawczyk-Stańdo D. (2003): The use of quasi-red and quasi-yellow nonobtuse refinements in the solution of 2-D electromagnetic, PDE's, In: Optimization and inverse problems in electro-magnetism (M. Rudnicki and S. Wiak, Ed.). — Dordrecht, Kluwer, pp. 113-124.Google Scholar

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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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