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On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis

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Multivariate Approximation and Splines

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 125))

Abstract

We give an upper bound for the L ∞ condition number of the triangular Bernstein basis for polynomials of total degree at most n in s variables. The upper bound grows like (s + 1)n when n tends to infinity. Moreover the upper bound is independent of s for s ≥ n — 1.

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References

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Author information

Authors and Affiliations

  1. Institutt for informatikk, University of Oslo, P. O. Box 1080, Blindem, 0316, Oslo, Norway

    Tom Lyche

  2. Institut für angewandte Mathematik, Rheinische Friedrich-Wilhems-Universität Bonn, Wegelstr. 6, 53115, Bonn, Germany

    Karl Scherer

Authors
  1. Tom Lyche
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  2. Karl Scherer
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany

    Günther Nürnberger  & Guido Walz  & 

  2. Institut für Numerische Mathematik, Technische Universität Dresden, D-01062, Dresden, Germany

    Jochen W. Schmidt

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© 1997 Springer Basel AG

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Lyche, T., Scherer, K. (1997). On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_12

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  • DOI: https://doi.org/10.1007/978-3-0348-8871-4_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9808-9

  • Online ISBN: 978-3-0348-8871-4

  • eBook Packages: Springer Book Archive

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