Аннотация:

The paper proposes a direct method for the numerical solution of a two-dimensional coefficient inverse problem for a hyperbolic equation. The problem is reduced to solving a linear integral equation, after discretization of which a system of linear algebraic equations with a block-Toeplitz matrix is obtained. Algorithms for numerical solutions of the direct and inverse problems are constructed and analyzed. The singular numbers of the matrix are numerically investigated and it is shown that the number of matrix conditionality, which characterizes the degree of incorrectness of the problem, increases with the depth of the coefficient recovery and with the increase in the error in the data. It is shown that the number of harmonics to be restored is a regularization parameter. The algorithm for solving the inverse problem has been tested on an analytical solution.