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 Eurasian Journal of Mathematical and Computer Applications: Year: Volume: Issue: Page: Find

 Eurasian Journal of Mathematical and Computer Applications, 2019, Volume 7, Issue 2, Pages 79–88 (Mi ejmca104)

Regularized Newton type method for retrieval of heavy water in atmosphere by IR–spectra of the solar light transmission

G. G. Skorikab, V. V. Vasinab

a Ural Federal University Lenin Avenue 51, Yekaterinburg 620000, Russia
b Institute of Mathematics and Mechanics UB RAS S.Kovalevskaya Str. 16, Yekaterinburg, 620990 Russia

Abstract: The inverse problem of reconstructing the vertical profiles of HDO/H$_2$O in the atmosphere by IR-spectra of solar light transmission is investigated. For solving this problem the two-stage method is suggested. On the first stage, we apply the Tikhonov regularization method with a special stabilizer. On the second stage, to approximate a solution of the regularized equation, we use a Fejér process of Newton-type. The convergence theorems are formulated, the Fejér property of iterations is substantiated and the results of numerical experiments for series of measured spectra are presented.

Keywords: inverse problem, heavy water, Tikhonov regularization, vertical profiles, Fejér process.

 Funding Agency Grant Number Russian Science Foundation 18-11-0024 The work was supported by the Russian Science Foundation, project no. 18-11-00024.

DOI: https://doi.org/10.32523/2306-6172-2019-7-2-79-88

Full text: PDF file (2851 kB)

Bibliographic databases:

MSC: 45Q05, 65R32.
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Citation: G. G. Skorik, V. V. Vasin, “Regularized Newton type method for retrieval of heavy water in atmosphere by IR–spectra of the solar light transmission”, Eurasian Journal of Mathematical and Computer Applications, 7:2 (2019), 79–88

Citation in format AMSBIB
\Bibitem{SkoVas19} \by G.~G.~Skorik, V.~V.~Vasin \paper Regularized Newton type method for retrieval of heavy water in atmosphere by IR–spectra of the solar light transmission \jour Eurasian Journal of Mathematical and Computer Applications \yr 2019 \vol 7 \issue 2 \pages 79--88 \mathnet{http://mi.mathnet.ru/ejmca104} \crossref{https://doi.org/10.32523/2306-6172-2019-7-2-79-88} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000470767100005} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067563374}