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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 1, Pages 57–79
DOI: https://doi.org/10.15372/SJNM20190105
(Mi sjvm701)
 

This article is cited in 13 scientific papers (total in 13 papers)

The Newton–Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data

A. V. Penenkoab

a Novosibirsk State University, st. Pirogova 2, Novosibirsk, 630090, Russia
b Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Akad. Lavrentjeva 6, Novosibirsk, 630090, Russia
References:
Abstract: The algorithms for solving the inverse source problem for the production–destruction type systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. The sensitivity operator and its discrete analogue on the basis of adjoint equations are constructed. This operator binds the perturbations in the unknown parameters of the model to those of the measured values. The operator allows one to construct a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. The Newton–Kantorovich type method with right-hand side $r$-pseudoinverse matrices is used to solve the equations. The algorithm is applied to solving the inverse source problem for the atmospheric impurities transformation model.
Key words: inverse source problem, big data, Newton–Kantorovich method, adjoint equations, sensitivity operator, $r$-pseudoinverse matrix, right inverse.
Funding agency Grant number
Russian Science Foundation 17-71-10184
Ministry of Education and Science of the Russian Federation
This work was supported by the Russian Science Foundation (project no. 17-71-10184 for the development of algorithms and their study) and by the Ministry of Education and Science of the Russian Federation (project no. 4.1.3, joint laboratories of NSU–NSC SB RAS for the vectorization and optimization of the software).
Received: 26.02.2018
Revised: 24.05.2018
Accepted: 05.10.2018
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 1, Pages 51–69
DOI: https://doi.org/10.1134/S1995423919010051
Bibliographic databases:
Document Type: Article
UDC: 517.988, 519.62
Language: Russian
Citation: A. V. Penenko, “The Newton–Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data”, Sib. Zh. Vychisl. Mat., 22:1 (2019), 57–79; Num. Anal. Appl., 12:1 (2019), 51–69
Citation in format AMSBIB
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\pages 57--79
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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