Linear rational interpolation and its application in approximation and boundary value problems

Jean Paul Berrut, Hans Mittelmann

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the case that a function with large gradients in the interior of an interval has to be approximated over this interval or that the pseudospectral method is used to compute a similar solution of an ordinary boundary value problem. In both cases we assume that the function has minimal continuity properties but can be evaluated anywhere in the given interval. The key idea is then to attach poles to the polynomial interpolant, respectively solution of the collocation problem to obtain a special rational function with poles whose location has been optimized suitably. In the first case, the max norm of the error is minimized while in the second, the same norm is minimized of the residual of the given differential equation. The algorithms are presented and discussed. Their effectiveness is demonstrated with numerical results.

Original languageEnglish (US)
Pages (from-to)527-544
Number of pages18
JournalRocky Mountain Journal of Mathematics
Volume32
Issue number2
StatePublished - Jun 2002

Fingerprint

Rational Interpolation
Linear Interpolation
Boundary Value Problem
Interval
Pole
Approximation
Norm
Pseudospectral Method
Interpolants
Special Functions
Collocation
Rational function
Interior
Differential equation
Gradient
Numerical Results
Polynomial

Keywords

  • Linear rational collocation
  • Linear rational interpolation
  • Pole optimization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Linear rational interpolation and its application in approximation and boundary value problems. / Berrut, Jean Paul; Mittelmann, Hans.

In: Rocky Mountain Journal of Mathematics, Vol. 32, No. 2, 06.2002, p. 527-544.

Research output: Contribution to journalArticle

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