A PRECISE ESTIMATION METHOD FOR LOCATIONS IN AN INVERSE LOGARITHMIC POTENTIAL PROBLEM FOR POINT MASS MODELS

A numerical method is discussed for an inverse logarithmic potential p roblem for a point mass model. We first show the relation between loca tions of point masses and Fourier expansion of the logarithmic potenti al, and show a method using discrete Fourier coefficients. Next a modi fied method is proposed based on a property of the discrete Fourier tr ansform of the logarithmic potential. We give error estimates for our modified method, and compare it with the method using only discrete Fo urier coefficients. Numerical examples illustrate the applicability an d advantages of our modified method