Two-stage method for solving systems of nonlinear equations and its applications to the inverse atmospheric sounding problem
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 17-20
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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.
Keywords:
nonlinear system, regularization, iterative process, infrared spectrum, atmospheric remote sounding, HDO retrieval.
@article{DANMA_2020_494_a3,
author = {V. V. Vasin and G. G. Skorik},
title = {Two-stage method for solving systems of nonlinear equations and its applications to the inverse atmospheric sounding problem},
journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
pages = {17--20},
year = {2020},
volume = {494},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DANMA_2020_494_a3/}
}
TY - JOUR AU - V. V. Vasin AU - G. G. Skorik TI - Two-stage method for solving systems of nonlinear equations and its applications to the inverse atmospheric sounding problem JO - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ PY - 2020 SP - 17 EP - 20 VL - 494 UR - http://geodesic.mathdoc.fr/item/DANMA_2020_494_a3/ LA - ru ID - DANMA_2020_494_a3 ER -
%0 Journal Article %A V. V. Vasin %A G. G. Skorik %T Two-stage method for solving systems of nonlinear equations and its applications to the inverse atmospheric sounding problem %J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ %D 2020 %P 17-20 %V 494 %U http://geodesic.mathdoc.fr/item/DANMA_2020_494_a3/ %G ru %F DANMA_2020_494_a3
V. V. Vasin; G. G. Skorik. Two-stage method for solving systems of nonlinear equations and its applications to the inverse atmospheric sounding problem. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 17-20. http://geodesic.mathdoc.fr/item/DANMA_2020_494_a3/
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