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The coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand-Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand-Levitan equation. We obtain the estimation of the solution of the Gelfand-Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented. [ABSTRACT FROM AUTHOR]

An inverse problem of reconstructing the two-dimensional coefficient of thewave 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 andmemory requirements. Results of numerical calculations are presented. [ABSTRACT FROM AUTHOR]