Advances in Computational Mathematics

, Volume 10, Issue 3, pp 343–365

Dyadic Hermite interpolation on a rectangular mesh

  • Serge Dubuc
  • Jean-Louis Merrien

DOI: 10.1023/A:1018943002601

Cite this article as:
Dubuc, S. & Merrien, JL. Advances in Computational Mathematics (1999) 10: 343. doi:10.1023/A:1018943002601


Given f and ∇f at the vertices of a rectangular mesh, we build an interpolating function f by a subdivision algorithm. The construction on each elementary rectangle is independent of any disjoint rectangle. From the Hermite data associated with the vertices of a rectangle R, the function f is defined on a dense subset of R. Sufficient conditions are found in order to extend f to a C1 function. Moreover, infinite products and generalized radii of matrices are used to study the convergence to a C1 function. This convergence depends on the five parameters introduced in the algorithm.

interpolation subdivision rectangular mesh generalized radii of matrices 41A05 63D05 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Serge Dubuc
    • 1
  • Jean-Louis Merrien
    • 2
  1. 1.Département de Mathématiques et de StatistiqueUniversité de MontréalMontréalCanada
  2. 2.INSA de RennesRennes CedexFrance

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