This paper is devoted to the following problem: Given an n-dimensional simplicial complex K, find a refinement K′ of K with the property: For arbitrary data wx ∈ℝ,βx ∈ℝn associated with the vertices x of K, there is a unique quadratic spline function φ with respect to K’, satisfying the Hermite interpolation conditions φ(x)=wx and gradφ(x)=βx for all vertices x of K. It is shown how to solve this problem in the 3-dimensional case, if there exists a certain dual cell complex of K. The underlying concepts however are independent of the number of variables.


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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Gerhard Heindl
    • 1
  1. 1.Fachbereich MathematikUniversität WuppertalWuppertal 1Germany

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