Determine whether maximal Puiseux-series interpolation is optimal

Determine whether fitting the maximal number of coefficients of the Puiseux series always gives the best endpoint approximation, or whether using more samples than fitted coefficients through a least-squares fit can provide a superior alternative.

Background

The endpoint approximation can use a truncated Puiseux series whose coefficients are determined by interpolation. The paper generally considers fitting as many coefficients as available samples, but notes that this choice may not be optimal in the presence of numerical sampling error, ill-conditioning, or computational costs associated with tracking additional points.

A proposed alternative is to obtain N samples and fit only the M<N leading Puiseux coefficients by least squares. The paper leaves unresolved whether the maximal-coefficient strategy is universally preferable to such a reduced least-squares fit.