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2007 | 17 | 2 | 157-164
Tytuł artykułu

Regularization parameter selection in discrete ill-posed problems - the use of the U-curve

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
17
Numer
2
Strony
157-164
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-12-08
(nieznana)
2006-12-15
poprawiono
2007-04-14
Twórcy
  • 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
Bibliografia
  • Groetsch N. (1984): The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind. - London: Pitman.
  • 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.
  • Hansen P.C. and O'Leary D.P. (1993): The use of the L-curve in the regularization of discrete ill-posed problems. - SIAM J. Sci. Comput., Vol.14, No.6, pp.487-1503.
  • Hansen P.C. (1993): Regularization Tools, a Matlab package for analysis and solution of discrete ill-posed problems. - Report UNIC-92-03
  • 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.
  • Lawson C.L. and Hanson R.J. (1974): Solving Least Squares Problems.- Englewood Cliffs, NJ: Prentice-Hall.
  • Neittaanmaki P., Rudnicki M. and Savini A. (1996): Inverse Problems and Optimal Design in Electry and Magnetism. - Oxford: Clarendon Press.
  • Regińska T. (1996): A regularization parameter in discrete ill-posed problems. - SIAM J. Sci. Comput., Vol.17, No.3, pp.740-749.
  • 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 electromagnetism (M. Rudnicki and S. Wiak, Ed.). - Dordrecht,Kluwer, pp.113-124.
  • Wahba G. (1977): Practical approximate solutions to linear operator equations when data are noisy.- SIAM J. Numer. Anal., Vol.14, No.4, pp.651-667
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv17i2p157bwm
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