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Communication Dans Un Congrès Année : 2011

A first constructive characterisation of all piecewise Chebyshevian splines suitable for approximation or design

Résumé

By piecewise Chebyshevian splines we mean splines with sections in different Extended Chebyshev spaces and with possibly connection matrices at the knots. In this general difficult framework (first considered by P.J. Barry in 96), existence of blossoms is known as a beautiful and powerful characterisation for a spline space to be suitable for Design (or Approximation as well). Nevertheless, beyond the analogue of the cubic spline case, up to now it remained a theoretical characterisation, not a really constructive one. In the present work, we give a surprisingly simple description of ALL piecewise Chebyshevian splines which do possess blossoms. It is a contructive characterisation in two ways:
  • firstly, at last we are now able to build in a simple way exactly all suitable piecewise Chebyshevian spline spaces, in any dimension and with any multiplicities;
  • secondly, a space of piecewise Chebyshevian splines being given, we are now able to answer the question "is it or not suitable for design?" Let us mention that the answer to the latter question is made possible by a recently published work in which we gave a constructive way to build all systems of weight functions which can be associated with a given Extended Chebyshev space on a closed bounded interval.
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    Dates et versions

    hal-00874997 , version 1 (20-10-2013)

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    • HAL Id : hal-00874997 , version 1

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    Marie-Laurence Mazure. A first constructive characterisation of all piecewise Chebyshevian splines suitable for approximation or design. ICMA2011 - International Conference on Multivariate Approximation, Sep 2011, Hagen, Germany. ⟨hal-00874997⟩
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