Rational interpolation through the optimal attachment of poles to the interpolating polynomial

Jean Paul Berrut, Hans Mittelmann

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.

Original languageEnglish (US)
Pages (from-to)315-328
Number of pages14
JournalNumerical Algorithms
Volume23
Issue number4
StatePublished - 2000

Fingerprint

Rational Interpolation
Pole
Poles
Interpolation
Polynomials
Polynomial
Markov's inequality
Centrobaric
Polynomial Interpolation
Interpolants
Vertex of a graph
Placement
Slope
Interpolate
Minimise
Norm
Interval
Alternatives

Keywords

  • Interpolation
  • Optimal interpolation
  • Rational interpolation

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Rational interpolation through the optimal attachment of poles to the interpolating polynomial. / Berrut, Jean Paul; Mittelmann, Hans.

In: Numerical Algorithms, Vol. 23, No. 4, 2000, p. 315-328.

Research output: Contribution to journalArticle

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