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Multivariate piecewise polynomials

Published online by Cambridge University Press:  07 November 2008

C. de Boor
C. de Boor
Affiliation:
Center for Mathematical SciencesUniversity of Wisconsin-MadisonMadison WI 53705USA, E-mail: deboor@cs.wisc.edu
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Extract

This article was supposed to be on ‘multivariate splines». An informal survey, taken recently by asking various people in Approximation Theory what they consider to be a ‘multivariate spline’, resulted in the answer that a multivariate spline is a possibly smooth piecewise polynomial function of several arguments. In particular the potentially very useful thin-plate spline was thought to belong more to the subject of radial basis funtions than in the present article. This is all the more surprising to me since I am convinced that the variational approach to splines will play a much greater role in multivariate spline theory than it did or should have in the univariate theory. Still, as there is more than enough material for a survey of multivariate piecewise polynomials, this article is restricted to this topic, as is indicated by the (changed) title.

Type
Research Article
Information
Acta Numerica , Volume 2 , January 1993 , pp. 65 - 109
Copyright
Copyright © Cambridge University Press 1993

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