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This article is cited in 2 scientific papers (total in 2 papers)
On a linear inverse potential problem with approximate data on the potential field on an approximately given surface
E. B. Laneev, E. Yu. Ponomarenko S.M. Nikol'skii Mathematical Institute,
Peoples Friendship University of Russia (RUDN University),
6 Miklukho Maklay St,
117198 Moscow, Russian Federation
Abstract:
An approximate solution of the linear inverse problem for the Newtonian potential for bodies of constant thickness is constructed. The solution is stable with respect to the error in the data on the potential field given on an inaccurately known surface. The problem is reduced to an integral equation of the first kind, the proof of the stability of the solution is based on the Tikhonov regularization method.
Keywords and phrases:
ill-posed problem, inverse problem for the potential, Sretenskiy class of bodies, method of Tikhonov regularization.
Received: 16.01.2022
Citation:
E. B. Laneev, E. Yu. Ponomarenko, “On a linear inverse potential problem with approximate data on the potential field on an approximately given surface”, Eurasian Math. J., 14:1 (2023), 55–70
Linking options:
https://www.mathnet.ru/eng/emj462 https://www.mathnet.ru/eng/emj/v14/i1/p55
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Abstract page: | 62 | Full-text PDF : | 30 | References: | 12 |
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