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Numerical Algorithms

, Volume 61, Issue 2, pp 291–313 | Cite as

Radial orthogonality and Lebesgue constants on the disk

  • Annie Cuyt
  • Irem Yaman
  • Bayram Ali Ibrahimoglu
  • Brahim Benouahmane
Original   Paper

Abstract

In polynomial interpolation, the choice of the polynomial basis and the location of the interpolation points play an important role numerically, even more so in the multivariate case. We explore the concept of spherical orthogonality for multivariate polynomials in more detail on the disk. We focus on two items: on the one hand the construction of a fully orthogonal cartesian basis for the space of multivariate polynomials starting from this sequence of spherical orthogonal polynomials, and on the other hand the connection between these orthogonal polynomials and the Lebesgue constant in multivariate polynomial interpolation on the disk. We point out the many links of the two topics under discussion with the existing literature. The new results are illustrated with an example of polynomial interpolation and approximation on the unit disk. The numerical example is also compared with the popular radial basis function interpolation.

Keywords

Polynomial interpolation Lebesgue constant Orthogonal polynomials Unit disk Several variables 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Annie Cuyt
    • 1
  • Irem Yaman
    • 2
  • Bayram Ali Ibrahimoglu
    • 1
    • 3
  • Brahim Benouahmane
    • 4
  1. 1.Department of Mathematics and Computer ScienceUniversiteit Antwerpen (CMI)AntwerpenBelgium
  2. 2.Department of Mathematics, Faculty of ScienceGebze Institute of TechnologyGebzeTurkey
  3. 3.Department of Mathematical EngineeringYıldız Technical UniversityIstanbulTurkey
  4. 4.Département de Mathématiques, Faculté des Sciences et TechniquesUniversité Hassan IIMohammadiaMorocco

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