Error Estimates and Convergence Rates for Variational Hermite Interpolation

AbstractThis 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 spaceChdetermined by givenr-CPDmfunctionh, is just theh-spline Hermite interpolant. The results on error estimation and convergence rate of theh-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