Least squares fitting with elliptic paraboloids

Abstract

In \cite{Sp4} we discussed the problem of fitting some rotated paraboloid to given measured data in 3-space. A numerical method was developed and numerical examples were given. Recently that method was used to fit some parabolic antenna filter \cite{Sp1}. In this connection the question arises whether this method could be extended for elliptic paraboloids needed for some medical application \cite{Sp2}. We show how this could be done and recommend a numerical method more difficult but similar to that one in [4].