Orthogonal rational functions and quadrature on the real half line

Authors:
A. Bultheel;P. González-Vera;E. Hendriksen;Olav Njåstad
Affiliations:
Department of Computer Science, K. U. Leuven, Belgium;Department of Mathematical Analysis, Univ. La Laguna, Tenerife, Spain;Department of Mathematics, University of Amsterdam, The Netherlands;Department of Mathematical Science, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
Journal of Complexity
Year:
2003

Citing 2
Cited 6

Generalized Gaussian quadrature formulas

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Quadrature on the half line and two-point Pade´ approximants to Stieltjes functions: subtitle: Part III. The unbounded case

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Orthogonal rational functions on the real half line with poles in [-∞, 0]

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
The computation of orthogonal rational functions on an interval

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Orthogonal rational functions on the real half line with poles in [-∞,0]

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
The computation of orthogonal rational functions on an interval

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Olav Njåstad

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Full length article: An extension of the associated rational functions on the unit circle

Journal of Approximation Theory

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Abstract

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximants is discussed.