Abstract:
In this paper, we propose a regular iterative method of identifying a numerical parameter in the kernel of the integral equation of the first kind of the convolution type. It is shown that an unambiguous identification of the parameter is possible when an exact solution has discontinuities of the first kind. The convergence theorem is proved, and an example of the equation with a parameter, for which the method constructed is applicable, is given.
Key words:
ill-posed problems, localization of singularities, equation of the first kind, parameter identification.
Citation:
T. V. Antonova, “Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities”, Sib. Zh. Vychisl. Mat., 18:2 (2015), 107–120; Num. Anal. Appl., 8:2 (2015), 89–100
\Bibitem{Ant15}
\by T.~V.~Antonova
\paper Methods of identifying a~parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities
\jour Sib. Zh. Vychisl. Mat.
\yr 2015
\vol 18
\issue 2
\pages 107--120
\mathnet{http://mi.mathnet.ru/sjvm570}
\crossref{https://doi.org/10.15372/SJNM20150201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3491690}
\elib{https://elibrary.ru/item.asp?id=23463691}
\transl
\jour Num. Anal. Appl.
\yr 2015
\vol 8
\issue 2
\pages 89--100
\crossref{https://doi.org/10.1134/S1995423915020019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84930661838}
Linking options:
https://www.mathnet.ru/eng/sjvm570
https://www.mathnet.ru/eng/sjvm/v18/i2/p107
This publication is cited in the following 1 articles:
Ya. N. Gusenitsa, “Solution of the Nonparametric Identification Equation in a Dynamic System Based on the Hyperdelta Approximation”, J. Mach. Manuf. Reliab., 51:1 (2022), 80
Citation in format AMSBIB
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