COMPUTING A STABLE LEAST SQUARES SOLUTION TO INVERSE PROBLEM FOR A PLANAR NEWTONIAN POTENTIAL

THE EXTERIOR INVERSE PROBLEM FOR A PLANAR Newtonian potential is considered. The external logarithmic potential of a body of unit density and of cylindrical geometry is assumed known on a circle of observation of radius R. The body is assumed to lie within a circle of radius D (D less than R) and to be star-shaped relative to the origin. The problem is to find the shape of the body. In order to avoid possible problems of nonexistence of a true solution, the problem is recast into least squares form. After discretization, the resulting system of nonlinear equations may be solved by Bewton's iterative method. This paper contains a report of some computer experiments in solving this problem, as well as a brief discussion of some theoretical aspects of the method.