Least squares data fitting with implicit functions

This paper discusses the computational problem of fitting data by an implicitly defined function depending on several parameters. The emphasis is on the technique of algebraic fitting of f(x, y; p) = 0 which can be treated as a linear problem when the parameters appear linearly. Various constraints completing the problem are examined for their effectiveness and in particular for two applications: fitting ellipses and functions defined by the Lotka-Volterra model equations. Finally, we discuss geometric fitting as an alternative, and give examples comparing results.