Numerische Mathematik

, Volume 107, Issue 2, pp 315-331

First online:

Barycentric rational interpolation with no poles and high rates of approximation

  • Michael S. FloaterAffiliated withCentre of Mathematics for Applications, Department of Informatics, University of Oslo Email author 
  • , Kai HormannAffiliated withDepartment of Informatics, Clausthal University of Technology

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It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no real poles and arbitrarily high approximation orders on any real interval, regardless of the distribution of the points. These interpolants depend linearly on the data and include a construction of Berrut as a special case.

Mathematics Subject Classification (2000)

65D05 41A05 41A20 41A25