Modified Moments and Orthogonal Rational Functions | Zendy

Van Deun J. | Zendy; Bultheel A. | Zendy

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Modified Moments and Orthogonal Rational Functions

Author(s) -

Van Deun J.,

Bultheel A.

Publication year - 2004

Publication title -

applied numerical analysis & computational mathematics

Language(s) - English

Resource type - Journals

eISSN - 1611-8189

pISSN - 1611-8170

DOI - 10.1002/anac.200410009

Subject(s) - orthogonal polynomials , mathematics , computation , rational function , moment (physics) , quadrature (astronomy) , measure (data warehouse) , discrete orthogonal polynomials , connection (principal bundle) , pure mathematics , algebra over a field , algorithm , computer science , physics , geometry , classical mechanics , database , optics

In a series of articles [9, 10, 11] about the numerical computation of orthogonal polynomials on a subset of the real line, Gautschi shows that computing orthogonal polynomials starting from the moments μ k = ∫ x k dμ ( x ) of the measure is generally an ill‐conditioned problem. However, in [10] an alternative approach is presented, based on so‐called modified moments, which works better in certain situations. In this paper we generalize these results to the computation of orthogonal rational functions and provide a new modified moment algorithm, based on the connection between modified moments and interpolatory quadrature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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