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Interpolatory and variation-diminishing properties of generalized B-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 Dundee, Dundee
S. L. Lee
Affiliation:
School of Mathematical Sciences, University of Science of Malaysia, Penang, Malaysia
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Synopsis

We consider classes of functions satisfying certain simple criteria of sign and smoothness and a decomposition property. It is known that these properties are possessed by Chebysheffian B-splines and it is shown here that they are also possessed by certain trigonometric B-splines. For such a class of functions, we derive a variation-diminishing property and analyse interpolation both on a finite set of nodes and on an infinite, periodically spaced set of nodes. The results are also applied to interpolation by complex polynomial splines on the circle.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 249 - 259
Copyright
Copyright © Royal Society of Edinburgh 1984

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