Adaptive point shifts in rational approximation with optimized denominator

J. P. Berrut, Hans Mittelmann

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.

Original languageEnglish (US)
Pages (from-to)81-92
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume164
Issue number1
DOIs
StatePublished - Mar 1 2004

Fingerprint

Rational Approximation
Denominator
Pole
Poles
Interpolants
Centrobaric
Rational Interpolation
Interval
Shock
Interpolation
Differential equations
Polynomials
Differential equation
Gradient
Derivatives
Derivative
Polynomial
Approximation
Vertex of a graph

Keywords

  • Interpolation
  • Optimal interpolation
  • Point shifts
  • Rational approximation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Adaptive point shifts in rational approximation with optimized denominator. / Berrut, J. P.; Mittelmann, Hans.

In: Journal of Computational and Applied Mathematics, Vol. 164, No. 1, 01.03.2004, p. 81-92.

Research output: Contribution to journalArticle

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