Abstract
The coefficient inverse problem for the acoustic equation is considered. We propose the method for reconstructing the density based on the N-approximation by the finite system of one-dimensional problems and the two-dimensional M. G. Krein approach. The two-dimensional analogue of the M. G. Krein approach is applied to reduce the non-linear inverse problem to a family of linear integral equations. We consider the fast algorithm for solving the relevant linear system, based on using the block-Toeplitz structure of the matrix. The algorithm applied to the M. G. Krein equation allows to obtain the solution of the whole family of the integral equations by solving only one linear system. Results of numerical calculations are presented.
Funding source: RFBR
Award Identifier / Grant number: 14-01-00208
Funding source: RFBR
Award Identifier / Grant number: 15-01-09230
Funding source: the Ministry of Education and Science of the Russian Federation and the Ministry of Education and Science of the Republic of Kazakhstan
Award Identifier / Grant number: MES 1760/GF: project NTP 04.03.02 “Creating methodological basis of geological-geophysical studies of focal zones UNE in igneous rocks”
Funding source: Russian Science Foundation
Award Identifier / Grant number: 14-01-000659
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