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Blossoming and Divided Difference

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Book cover Geometric Modelling

Part of the book series: Computing ((COMPUTING,volume 14))

Abstract

Blossoming and divided difference are shown to be characterized by a similar set of axioms. But the divided difference obeys a cancellation postulate which is not included in the standard blossoming axioms. Here the blossom is extended to incorporate a new set of parameters along with a cancellation axiom. Both the standard blossom and the divided difference operator are special cases of this new extended blossom. It follows that these dual functionals all satisfy a similar collection of formulas and identities, including a Marsden identity, a recurrence relation, a degree elevation formula, a multirational property, a differentiation identity, and expressions for partial derivatives with respect to their parameters. In addition, formulas are presented that express the divided differences of polynomials in terms of the blossom. Canonical examples are provided for the blossom, the divided difference, and the extended blossom, and general proof procedures are developed based on these characteristic functions.

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Author information

Authors and Affiliations

  1. Department of Computer Science - MS-132, Rice University, 6100 Main Street, 77005-1892, Houston, TX, USA

    R. Goldman

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  1. R. Goldman
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, TU Chemnitz, Chemnitz, Germany

    Guido Brunnett

  2. Institut für Informatik und angewandte Mathematik, Universität Bern, Bern, Switzerland

    Hanspeter Bieri

  3. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ, USA

    Gerald Farin

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© 2001 Springer-Verlag Wien

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Goldman, R. (2001). Blossoming and Divided Difference. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_9

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  • DOI: https://doi.org/10.1007/978-3-7091-6270-5_9

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83603-3

  • Online ISBN: 978-3-7091-6270-5

  • eBook Packages: Springer Book Archive

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