AN ESTIMATION METHOD FOR THE NUMBER OF POINT MASSES IN AN INVERSE LOGARITHMIC POTENTIAL PROBLEM USING DISCRETE FOURIER-TRANSFORM

A numerical method is discussed for the estimation of the number of point masses in an inverse logarithmic potential problem. We consider the case of some pieces of point masses being located in an ''indeterminacy domain,'' and consider a problem to estimate the number of point masses using observation data of the logarithmic potential on the boundary. A uniqueness theorem is derived for this problem from an algebraic relation between parameters of a point mass model and Fourier coefficients of the logarithmic potential. Applying this theorem, we propose a numerical method for our problem using a criterion function computed from the discrete Fourier transform. The applicability of our method is illustrated by numerical examples.