Abstract:
In this paper, two flow charts for solving the same inverse problem by an optimization method are presented. On numerical examples it is shown that the first flow chat often used by researchers requires much more computer costs than the second one. This is because of the necessity of using a fine net and due to an increase in the number of minimization iterations of the residual functional for its decrease up to a certain value.
Citation:
A. L. Karchevsky, “A correct flow chart for numerical solution to an inverse problem by optimization method”, Sib. Zh. Vychisl. Mat., 11:2 (2008), 139–149; Num. Anal. Appl., 1:2 (2008), 114–122
\Bibitem{Kar08}
\by A.~L.~Karchevsky
\paper A~correct flow chart for numerical solution to an inverse problem by optimization method
\jour Sib. Zh. Vychisl. Mat.
\yr 2008
\vol 11
\issue 2
\pages 139--149
\mathnet{http://mi.mathnet.ru/sjvm39}
\transl
\jour Num. Anal. Appl.
\yr 2008
\vol 1
\issue 2
\pages 114--122
\crossref{https://doi.org/10.1134/S1995423908020031}
Linking options:
https://www.mathnet.ru/eng/sjvm39
https://www.mathnet.ru/eng/sjvm/v11/i2/p139
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K.R. Aida-zade, V.M. Abdullayev, “APPROACH TO DETERMINING THE PARAMETERS OF A DYNAMIC SYSTEM UNDER NONLOCAL HIGH-ORDER OVERDETERMINATION CONDITIONS”, KCA, 2024, 125
E. B. Sibiryakov, “Coefficient inverse problem for the Helmholtz equation”, Russian Journal of geophysical technologies, 2023, no. 3, 77
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A. V. Penenko, “Consistent numerical schemes for solving nonlinear inverse source problems with the gradient-type algorithms and the Newton–Kantorovich methods”, Num. Anal. Appl., 11:1 (2018), 73–88
Rysbaiuly B., Yunicheva N., Rysbayeva N., “An Iterative Method to Calculate the Thermal Characteristics of the Rock Mass With Inaccurate Initial Data”, Open Eng., 6:1 (2016), 627–636
A. V. Penenko, “Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods”, Num. Anal. Appl., 5:4 (2012), 326–341
V. V. Vasin, V. N. Dubinin, V. G. Romanov, “Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke””, Sib. elektron. matem. izv., 5 (2008), 427–439
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