Polynomial Interpolation of Real Functions I: Interpolation in an Interval.

摘要

This paper is the first in a series to analyse the accuracy of polynomial interpolation of functions and its dependence on the locations of the interpolation nodes. It surveys known results for polynomial interpolation in an interval. It also introduces the concept of the Minimal Interpolation Sets which are the 'optimal' interpolation sets. New results concerning the properties of the minimal sets as well as procedures for locating the minimal sets are presented. The table for the minimal sets in the L- norm is given. An adaptive scheme for determining the interpolation order is also presented. Examples show the efficacy of this approach.