Mathematical Sciences: Faculty Publications

Convergence of Local Variational Spline Interpolation

Document Type

Article

Publication Date

5-1-2008

Publication Title

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2007.10.022

ISSN

0022-247X

Abstract

In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local variational spline increases. By piecing together these locally defined splines, one can obtain a very good C0 approximation of the global variational spline. Finally we generalize this idea to approximate global tensor product B-spline interpolatory surfaces.

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