This work is devoted to numerical experiments for multidimensional
Spectral Inverse Problems. We check the efficiency of the algorithm
based on the BC-method, which exploits relations between Boundary
Control Theory and Inverse Problems. As a test, the problem for an
ellipse is considered. This case is of interest due to the fact
that a field of normal geodesics loses regularity on a nontrivial
separation set. The main result is that the BC-algorithm works
quite successfully in spite of this complication. A theoretical
introduction to the BC-method is included.