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Two-Stage Method for Solving Systems of Nonlinear Equations and Its Applications to the Inverse Atmospheric Sounding Problem

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Abstract

For an overdetermined system of nonlinear equations, a two-stage method is suggested for constructing an error-stable approximate solution. The first stage consists in constructing a regularized set of approximate solutions for finding normal quasi-solutions of the original system. At the second stage, the regularized quasi-solutions are approximated using an iterative process based on square approximation of the Tikhonov functional and a prox-method. For this Newton-type method, a convergence theorem is proved and the Fejér property of the iterations is established. Additionally, the two-stage method is applied to the inverse problem of reconstructing heavy water (HDO) in the atmosphere from infrared spectra of solar light transmission.

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ACKNOWLEDGMENTS

We are grateful to K.G. Gribanov for his help in implementing the FIRE-ARMS code for computing model IR spectra and to N.V. Rokotyan for placing at our disposal IR spectra measured by the FTIR spectrometer at the Kourovka Astronomical Observatory.

Funding

Vasin acknowledges the support of the Russian Science Foundation, project no. 18-11-00024.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620990, Yekaterinburg, Russia

    V. V. Vasin & G. G. Skorik

  2. Ural Federal University, 620002, Yekaterinburg, Russia

    V. V. Vasin & G. G. Skorik

Authors
  1. V. V. Vasin
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  2. G. G. Skorik
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Corresponding authors

Correspondence to V. V. Vasin or G. G. Skorik.

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Translated by I. Ruzanova

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Vasin, V.V., Skorik, G.G. Two-Stage Method for Solving Systems of Nonlinear Equations and Its Applications to the Inverse Atmospheric Sounding Problem. Dokl. Math. 102, 367–370 (2020). https://doi.org/10.1134/S1064562420050439

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  • DOI: https://doi.org/10.1134/S1064562420050439

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