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Total positivity and the existence of piecewise exponential B-splines

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Abstract

We give necessary and sufficient conditions for the total positivity of certain connection matrices arising in piecewise exponential spline spaces. These total positivity conditions are sufficient for existence of B-splines in such spaces, but they are far from being necessary. We give a necessary and sufficient condition for existence of B-splines in the case of piecewise exponential spline spaces with only two differential operators, which eventually leads to a necessary condition for any piecewise exponential spline spaces.

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Author information

Authors and Affiliations

  1. Institutt for informatikk and CMA, Universitetet i Oslo, P.B. 1053, Blindern, 0316, Oslo, Norway

    Tom Lyche

  2. Laboratoire de Modélisation et Calcul (LMC-IMAG), Université Joseph Fourier, BP 53, 38041, Grenoble cedex, France

    Marie-Laurence Mazure

Authors
  1. Tom Lyche
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  2. Marie-Laurence Mazure
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Additional information

Communicated by M. Gasca

Dedicated to Professor Charles A. Micchelli for his 60th birthday

Mathematics subject classifications (2000)

65D17, 65D07, 41A15, 41A50.

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Lyche, T., Mazure, ML. Total positivity and the existence of piecewise exponential B-splines. Adv Comput Math 25, 105–133 (2006). https://doi.org/10.1007/s10444-004-7633-0

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  • DOI: https://doi.org/10.1007/s10444-004-7633-0

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