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 po int masses in an inverse logarithmic potential problem. We consider th e case of some pieces of point masses being located in an ''indetermin acy domain,'' and consider a problem to estimate the number of point m asses using observation data of the logarithmic potential on the bound ary. A uniqueness theorem is derived for this problem from an algebrai c relation between parameters of a point mass model and Fourier coeffi cients of the logarithmic potential. Applying this theorem, we propose a numerical method for our problem using a criterion function compute d from the discrete Fourier transform. The applicability of our method is illustrated by numerical examples.