Abstract
An inverse problem of reconstructing the two-dimensional coefficient of the wave equation is solved by a stochastic projection method. We apply the Gel'fand–Levitan approach to reduce the nonlinear inverse problem to a family of linear integral equations. The stochastic projection method is applied to solve the relevant linear system. We analyze the structure of the problem to increase the efficiency of the method by constructing an improved initial approximation. A smoothing spline is used to treat the random errors of the method. The method has low cost and memory requirements. Results of numerical calculations are presented.
Funding source: RFBR
Award Identifier / Grant number: 15-01-09230
Funding source: Ministry of Education and Science of the Russian Federation
Funding source: RFBR
Award Identifier / Grant number: 15-01-00977
Funding source: Ministry of Education and Science of the Republic of Kazakhstan
Award Identifier / Grant number: 1746/GF “Theory and numerical methods for solving inverse and ill-posed problems of natural sciences”
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