Orthogonal rational functions and quadrature on an interval

  • Authors:

  • J. Van Deun;A. Bultheel

  • Affiliations:

  • Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium;Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
  • Year:
  • 2003

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Abstract

Rational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of arbitrary complex poles and study orthogonality on a finite interval. The zeros of the orthogonal rational functions are shown to satisfy a quadratic eigenvalue problem. In the case of real poles, these zeros are used as nodes in the quadrature formulas.