The computation of orthogonal rational functions and their interpolating properties | Zendy

Adhemar Bultheel | Zendy; Pablo González-Vera | Zendy; Erik Hendriksen | Zendy; Olav Njåstad | Zendy

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The computation of orthogonal rational functions and their interpolating properties

Author(s) -

Adhemar Bultheel,

Pablo González-Vera,

Erik Hendriksen,

Olav Njåstad

Publication year - 1992

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/bf02142207

Subject(s) - mathematics , unit circle , rational function , orthogonal polynomials , infinity , theory of computation , degree (music) , complex plane , unit disk , pure mathematics , elliptic rational functions , computation , combinatorics , mathematical analysis , algorithm , physics , elliptic curve , acoustics , quarter period

We shall consider nested spaces L_n, n=0,1,2,... of rational functions with n prescribed poles outside the unit disk of the complex plane. We study orthogonal basis functions of these spaces for a general positive measure on the unit circle. In the special case where all poles are placed at infinity, L_n = P_n, the polynomials of degree at most n. Thus the present paper is a study of orthogonal rational functions, which generalize the orthogonal Szegö polynomials. In this paper we shall concentrate on the functions of the second kind which are natural generalizations of the corresponding polynomials.status: publishe

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