Kergin interpolation

(aka Real and complex mean value interpolation)

This page is dedicated to Kergin interpolation, and more generally to the scale of mean value interpolations (which includes Hakopian interpolation). These interpolation schemes, though not of great practical interest (since the interpolation conditions include various integrals of derivatives), are of theoretical interest because of their close connection with Hermite interpolation (and a widespread interest in developing a theory of multivariate polynomial interpolation).

Complex Kergin interpolation

Most of the recent work involves complex Kergin interpolation. The issues considered so far, are what conditions on the geometry of the domain are necessary and sufficient for mean value interpolants to be defined on holomorphic functions, and under what conditions does the sequence of interpolants converge locally uniformly to the function being approximated (as the number of points increases). People working on such questions include

Representing mean value interpolants and L_p-error bounds

Other work includes representing mean value interpolants (in terms of the interpolation conditions), obtaining L_p-error bounds for the interpolants, and estimating the uniform norm of the mean value interpolation operator. People working on such questions include


This document is maintained by Shayne ( Last Modified: .