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Optimally Stable Multivariate Bases

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Abstract

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.

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Authors and Affiliations

  1. Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, 0316, Oslo, Norway

    T. Lyche

  2. Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009, Zaragoza, Spain

    J.M. Peña

Authors
  1. T. Lyche
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  2. J.M. Peña
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Lyche, T., Peña, J. Optimally Stable Multivariate Bases. Advances in Computational Mathematics 20, 149–159 (2004). https://doi.org/10.1023/A:1025863309959

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