Direct method for solving the inverse coefficient problem for elliptic equation with piecewise constant coefficients

Some direct numerical method is presented for solving the inverse coefficient problem for an elliptic equation with piecewise constant coefficients. It is assumed that the discontinuity points of the coefficients are known. The algorithm is based on the theory of spectral problems of linear algebra and the application of finite-difference methods for solving the elliptic equations. The values (measurements) of the solution at the discontinuity points of the coefficients are used as additional information. In the case of unperturbed additional information, the coefficients are reconstructed precisely.