Piecewise-Quartics and Exponential Parameterization for Interpolating Reduced Data

We examine the asymptotics of a piecewise-quartic Lagrange interpolation used to fit reduced data in arbitrary Euclidean space which are sampled more-or-less uniformly. The unknown interpolation knots are guessed here according to the so-called exponential parameterization which depends on a single parameter lambda is an element of [0, 1]. In this work we demonstrate numerically an abrupt discontinuity in the quality of the discussed interpolation scheme yielding a slow linear convergence order for all lambda is an element of [0, 1). On the other hand, as well-known the quality of the curve approximation for lambda = 1 sharply increases to the fast sharp quartic order which can be further accelerated for special subfamilies of more-or-less uniform samplings.