Error estimates and convergence rates for variational hermite interpolation

Abstract

This paper considers the variational problem of Hermite interpolation and its error bounds. The optimal Hermite interpolant, which minimises the semi-norm of the reproducing kernel Hilbert space Ch determined by given r-CPDm function h, is just the h-spline Hermite interpolant. The results on error estimation and convergence rate of the h-spline interpolant generalise those of W. R. Madych and S. A. Nelson (1988, Approx. Theory Appl. 4, 77-89; 1990, Math. Comp. 54, 211-230), Z. Wu and R. Schabach (1993, IMA J. Numer. Anal. 13, 13-27), and W. Light and H. Wayne (1994, in "Approximation Theory, Wavelets and Applications" (S. P. Singh, Ed.), pp. 215-246, Kluwer Academic, Dordrecht/Norwell, MA) to the case of Hermite interpolation. © 1998 Academic Press.