Toeplitz Matrices in the BC-Method for the Plane Domains

The BC-method is the approach to inverse problems based on their connection with control theory and theory of systems. The main fragment of its numerical implementation is the matrix inversion of the so-called connecting operator. In multidimensional problems, its matrix is ill-conditioned and large in size, which yields the rapid growth of the volume of computations. The paper reveals block-Toeplitz structure of this matrix, using which one can significantly reduce the amount of computations.