Interpolation - as bad as it gets
by
Terry Mills
La Trobe University
Coauthors: P. Vértesi

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. This talk will review the place of this classical result in approximation theory. The main new result presented in this talk is an extension of their theorem. In particular, we will show that this divergence phenomenon occurs for odd higher order Hermite-Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

Date received: September 2, 1998