Orthogonal rational functions and quadrature on an interval

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2003-04, Vol.153 (1-2), p.487-495
Main Authors: Van Deun, J., Bultheel, A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Orthogonal rational functions
Quadratic eigenvalue problem
Quadrature
Sciences and techniques of general use
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00598-8