C2 piecewise cubic quasi-interpolants on a 6-direction mesh

O. Davydov, P. Sablonnière

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8 Citations (Scopus)
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We study two kinds of quasi-interpolants (abbr. QI) in the space of C2 piecewise cubics in the plane, or in a rectangular domain, endowed with the highly symmetric triangulation generated by a uniform 6-direction mesh. It has been proved recently that this space is generated by the integer translates of two multi-box splines. One kind of QIs is of differential type and the other of discrete type. As those QIs are exact on the space of cubic polynomials, their approximation order is 4 for sufficiently smooth functions. In addition, they exhibit nice superconvergent properties at some specific points. Moreover, the infinite norms of the discrete QIs being small, they give excellent approximations of a smooth function and of its first order partial derivatives. The approximation properties of the QIs are illustrated by numerical examples.
Original languageEnglish
Pages (from-to)528-544
Number of pages16
JournalJournal of Approximation Theory
Issue number3
Early online date2 Oct 2009
Publication statusPublished - 31 Mar 2010


  • bivariate splines
  • quasi-interpolation
  • 6-direction mesh


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