TY - JOUR

T1 - Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem

AU - Kabanikhin, Sergey I.

AU - Novikov, Nikita S.

AU - Oseledets, Ivan V.

AU - Shishlenin, Maxim A.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - fast Toeplitz algorithm

KW - Gelfand-Levitan method

KW - Inverse problems

KW - M. G. Krein equation

UR - http://www.scopus.com/inward/record.url?scp=84949755684&partnerID=8YFLogxK

U2 - 10.1515/jiip-2015-0083

DO - 10.1515/jiip-2015-0083

M3 - Article

AN - SCOPUS:84949755684

VL - 23

SP - 687

EP - 700

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 6

ER -