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Vertex Splines and Their Applications to Interpolation of Discrete Data

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Computation of Curves and Surfaces

Part of the book series: NATO ASI Series ((ASIC,volume 307))

Abstract

It is well known that B-splines in one variable play a central role in the theory of spline functions. However, although there are various generalizations of the notion of B-splines to the multi-variable setting in the literature, very little is known at this writing on the structure and theory of all compactly supported smooth piecewise polynomial functions on a preassigned grid partition Δ in ℝs, s > 1, unless Δ is perfectly regular. While we don’t have much to offer to the general theory, we will be satisfied with the study of those compactly supported ones with each support containing at least one common vertex and with the interior of the support containing at most one vertex of Δ. These functions are called vertex splines. The objective of this presentation is to give a brief description of the notion of vertex splines and to discuss their applications to interpolation of discrete data with or without constraints.

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Author information

Authors and Affiliations

  1. Center for Approximation Theory, Texas A&M University, College Station, TX, 77843, USA

    Charles K. Chui

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  1. Charles K. Chui
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Editor information

Editors and Affiliations

  1. Institut für Mathematik I, Freie Universität, Berlin, Germany

    Wolfgang Dahmen

  2. Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

    Mariano Gasca

  3. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA

    Charles A. Micchelli

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© 1990 Kluwer Academic Publishers

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Chui, C.K. (1990). Vertex Splines and Their Applications to Interpolation of Discrete Data. In: Dahmen, W., Gasca, M., Micchelli, C.A. (eds) Computation of Curves and Surfaces. NATO ASI Series, vol 307. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2017-0_5

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  • DOI: https://doi.org/10.1007/978-94-009-2017-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7404-9

  • Online ISBN: 978-94-009-2017-0

  • eBook Packages: Springer Book Archive

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