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Cardinal interpolation by Dm-splines

Published online by Cambridge University Press:  14 November 2011

T. N. T. Goodman  and
S. L. Lee
T. N. T. Goodman
Affiliation:
Department of Mathematical Sciences, University of DundeePenang, Malaysia
S. L. Lee
Affiliation:
School of Mathematical Sciences, University of Science of Malaysia, Penang, Malaysia
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Synopsis

Duchon (1978) considered interpolation in ℝn by “Dm-splines”, which are interpolating functions having, in a sense, minimum energy. The purpose of this paper is to consider the analogous interpolation at the lattice of points in ℝn with integer co-ordinates, generalising aspects of Schoenberg's (1973) theory of cardinal spline interpolation. Following Schoenberg, we prove that higher order “basic” splines can be written as convolutions of lower order ones, using a new notion of convolution due to Jones (1982).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 149 - 161
Copyright
Copyright © Royal Society of Edinburgh 1983

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