Nuclear Physics and Atomic Energy

ядерна ф≥зика та енергетика
Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English, Russian
  Periodicity: 4 times per year

  Open access peer reviewed journal


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Nucl. Phys. At. Energy 2019, volume 20, issue 1, pages 96-102.
Section: Engineering and Methods of Experiment.
Received: 22.11.2018; Accepted: 17.04.2019; Published online: 26.06.2019.
PDF Full text (ru)
https://doi.org/10.15407/jnpae2019.01.096

Accounting for apparatus function when registering experimental data: peculiarity of choosing regularization parameter by L-curve criterion at deconvolution of the spectrum

A. M. Sokolov*

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

*Corresponding author. E-mail address: amsklv@i.ua

Abstract: Within the framework of the problem of spectrum deconvolution, variant of the choice of the regularization parameter by criterion of the L-curve, based on the displacement along the points of the L-curve graph, is proposed. An analysis of dependencies on which the L-curve based is done. The L-curve itself is interpreted as a graph of the complex function of the norm of a regularized solution from the residual, and its similarity to the graph of the residual is noted.

Keywords: apparatus function, spectrum, regularization method, L-curve criteria.

References:

1. A.N. Tikhonov, V.Ya. Arsenin. Methods for Solving Incorrect Tasks (Moskva: Nauka, 1979). (Rus) Google books

2. V.A. Morozov. Regular Methods for Solving Incorrectly Assigned Tasks (Moskva: Moscow State University Publishing House, 1974). (Rus) Google books

3. A.V. Goncharsky, A.M. Cherepashchuk, A.G. Yagola. Numerical Solutions of Astrophysics Inverse Problems (Moskva: Nauka, 1978). (Rus) Google books

4. J. Weese. A reliable and fast method for the solution of Fredholm integral equation of the first kind based on Tikhonov regularization. Computer Physics Communications 69 (1992) 99. https://doi.org/10.1016/0010-4655(92)90132-I

5. P.C. Hansen. The L-curve and its use in the numerical treatment of inverse problems. In: Computational Inverse Problems in Electrocardiography. Ed. P. Johnston (Southampton: WIT Press, 2001) p. 119. Book

6. P.C. Hansen, D.P. O'Leary. The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993) 1487. https://doi.org/10.1137/0914086

7. G. Rodriguez, D. Theis. An algorithm for estimating the optimal regularization parameter by the L-curve. Rendiconti di Matematica. Serie VII. 25 (2005) 69. http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2005(1)/69-84.pdf