On the theory of spline interpolation of values and derivatives

Speaker: Michael Floater, University of Oslo

Abstract: There is a remarkable and important result in univariate spline theory: spline interpolation over a sequence of points has a unique solution if and only if the i-th point is contained in the support of the i-th B-spline. This was essentially shown by Schoenberg and Whitney in 1953 and later generalized to the (equally important) case of Hermite interpolation: the interpolation of both values and derivatives by Karlin and Ziegler in 1966. Since then various approaches have been made to simplify the proof, by Schumaker and de Boor, among others, using techniques such as variation-diminishing, B-spline recursion and knot-insertion. Prof. Floater will try to give an overview of these approaches and try to land on a 'simplest' proof.

Biography: Michael Floater received a PhD in mathematics from Oxford University in 1988. He later worked for several years at SINTEF in Oslo, Norway, on various industrial projects, many of which involved geometric modelling. He has been at the University of Oslo since 2003, initially in the Department of Informatics, later in the Department of Mathematics. His research areas are numerical analysis, approximation theory, and geometric modelling.

Host: Prof. Kai Hormann