Geodesic
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, Tome 7 (2019) no. 2, pp. 79-88.

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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. 
@article{EJMCA_2019_7_2_a3,
     author = {G. G. Skorik and V. V. Vasin},
     title = {Regularized {Newton} type method for retrieval of heavy water in atmosphere by {IR{\textendash}spectra} of the solar light transmission},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {79--88},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a3/}
}
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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, Tome 7 (2019) no. 2, pp. 79-88. http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a3/