Inexact searches on the L-curve

Authors

  • Hugo Lara Urdaneta Universidad Centroccidental Lisandro Alvarado, Venezuela
  • Adalys Alvarez Universidad Nacional Abierta, Venezuela
  • Freddy Torrealba Anzola Universidad Centroccidental Lisandro Alvarado, Venezuela

Keywords:

III-posed problems, Thikonov regularization, L-curve, inexact searches

Abstract

In a Tikhonov regularization scheme to solve discrete linear ill-posed problems, selecting the parameter value is a key task. We use Wolfe inexact search on the L-curve to choose a λ regularization parameter value far from critical areas of the L-curve. Numerical results are shown comparing the inexact scheme with other exact searches.

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Author Biographies

  • Hugo Lara Urdaneta, Universidad Centroccidental Lisandro Alvarado, Venezuela

    Departamento de Investigaci´on de Operaciones, Universidad Centroccidental “Lisandro Alvarado”, Barquisimeto

  • Freddy Torrealba Anzola, Universidad Centroccidental Lisandro Alvarado, Venezuela

    Departamento de F´ısica, Universidad Centroccidental “Lisandro Alvarado”, Barquisimeto, Venezuela

References

M. E Gulliksson, P. Wedin. Using the Nonlinear L-curve and its Dual, Progress in Industrial Math., ECMI, pp. 162-170, Eds., L. Arkeryd, J. Bergh, P. Brenner, and R. Pettersson, B.G. Teubner Stuttgart, Leibniz, 1999.

P. C. Hansen. The L-curve and its use in the numerical treatment of inverse problems, Com-putational Inverse Problems in Electrocardiology, Ed. P. Johnston. Advances in Computational Bioengineering, 2001, Vol 5.

K. Holmstrom and J. Petersson, A review of the parameter estimation problem of fitting positive exponential sums to empirical data, Applied Mathematics and Computation, 2002, Vol 126, No 1, 31-61.

D. Krawczyk-Stando and M. Rudnicki, Regularization parameter selection in discrete ill-posed problems - the use of the U-curve, Int. J. Appl. Math. Comput. Sci. 2007, Vol 17, No. 2, 157-164.

S. Nash and A. Sofer, Linear and Nonlinear Programming. McGraw Hill. 1996.

T. Reginska, A regularization parameter in discrete ill-posed problems, SIAM J. Sci. Comput 1996, Vol 17, No 3, 740-749.

Publicaciones en Ciencias y Tecnologia Vol 3 nro 1 año 2009

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Published

2009-09-28

Issue

Vol. 3 No. 1 (2009): January-June

Section

Research Article

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How to Cite

[1]
“Inexact searches on the L-curve”, Publ.Cienc.Tecnol, vol. 3, no. 1, pp. 15–22, Sep. 2009, Accessed: Jul. 23, 2026. Available: https://revistas2.uclave.org/index.php/pcyt/article/view/1100