Numerical Algorithms

, Volume 12, Issue 2, pp 287–296 | Cite as

Regular points for Lagrange interpolation on the unit disk

  • Thomas Sauer
  • Yuan Xu


A set of points on the unit disk of the Euclidean plane is given, which admits unique Lagrange interpolation. The points have rotational symmetry and they form an example of natural lattices of Chung and Yao [2]. Properties of Lagrange interpolation with respect to these points are studied.


Lagrange interpolation two variables unit disk 

Subject classification

AMS(MOS) Primary: 41A05, 65D10 


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  1. [1]
    C. de Boor, A multivariate divided difference, in:Approximation Theory VIII, C.K. Chui and L.L. Schumaker, eds., World Scientific, 1995, to appear.Google Scholar
  2. [2]
    K.C. Chung and T.H. Yao, On lattices admitting unique Lagrange interpolation, SIAM J. Numer Anal. 14 (1977) 735–743.CrossRefGoogle Scholar
  3. [3]
    M. Gasca and J.I. Maeztu, On Lagrange and Hermite interpolation in ℝk, Numer. Math. 39 (1982) 1–14.CrossRefGoogle Scholar
  4. [4]
    C.A. Micchelli, A constructive approach to Kergin interpolation in ℝk: multivariate B-splines and Lagrange interpolation, Rocky Mountain J. Math. 10 (1979) 485–497.Google Scholar
  5. [5]
    Th. Sauer and Y. Xu, On multivariate Lagrange interpolation, Math. Comp. 64 (1995) 1147–1170.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Thomas Sauer
    • 1
  • Yuan Xu
    • 2
  1. 1.Mathematical InstituteUniversity Erlangen-NurembergErlangenGermany
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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