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Title: Zeroes of orthogonal polynomials by QD-algorithm (English)
Author: Fiala, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 14
Issue: 3
Year: 1969
Pages: 210-219
Summary lang: English
Summary lang: Czech
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Category: math
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Summary: In the paper a method for computing zeroes of orthogonal polynomials is presented. An algorithm is given for computing directly the top row of the QD-scheme for some recurrently defined polynomials. The algorithm is then applied to classical orthogonal polynomials. (English)
Keyword: numerical analysis
MSC: 65.50
idZBL: Zbl 0194.18304
idMR: MR0248976
DOI: 10.21136/AM.1969.103226
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Date available: 2008-05-20T17:45:12Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/103226
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Reference: [1] Крылов В. И.: Приближенное вычисление интегралов.Москва 1959. Zbl 1047.90504
Reference: [2] G. Szegö: Orthogonal polynomials.AMS, N.Y. 1959. MR 0106295
Reference: [3] H. Rutishauser: Der Quotienten-Differenzen-Algorithmus.Birkhäuser Verlag Basel/Stuttgart 1957. Zbl 0077.11103, MR 0089499
Reference: [4] H. Rutishauser: On a modification of the QD-algorithm with Graeffe-type convergence.Information Processing 1962, North-Holland, Amsterdam 1963, pp. 93-96. Zbl 0113.10702, MR 0251885
Reference: [5] J. Fiala: Řešení algebraických rovnic QD-algoritmem.Zpráva a program 7-07-04, VLD Praha, 1964.
Reference: [6] Айзенштад В. С., Крылов В. И., МетелъскийА. С.: Таблицы для численного преобразования Лапласа и вычисления интегралов вида $\int_0^{+\infty} x^s e^{-x} f(x) dx$.АН БССР Минск 1962.
Reference: [7] P. Rabinowitz, G. Weiss: Tables of Abscissas and weights for numerical evaluation of integrals of the form $\int_0^{+\infty} e^{-x} x^nf(x) dx$.Math. Tables and Other Aids to Соmр. 13 (1959) 285-293. MR 0107992
Reference: [8] Head, Wilson: Laguerre functions: Tables and properties.Proc. I.E.E., Part C, 103 (1956) 428.
Reference: [9] H. Wall: Analytic theory of continued fractions.N.Y. 1948. Zbl 0035.03601, MR 0025596
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