Zeroes of orthogonal polynomials by QD-algorithm

Jiří Fiala

Aplikace matematiky (1969)

  • Volume: 14, Issue: 3, page 210-219
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Fiala, Jiří. "Zeroes of orthogonal polynomials by QD-algorithm." Aplikace matematiky 14.3 (1969): 210-219. <http://eudml.org/doc/14594>.

@article{Fiala1969,
abstract = {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.},
author = {Fiala, Jiří},
journal = {Aplikace matematiky},
keywords = {numerical analysis},
language = {eng},
number = {3},
pages = {210-219},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Zeroes of orthogonal polynomials by QD-algorithm},
url = {http://eudml.org/doc/14594},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Fiala, Jiří
TI - Zeroes of orthogonal polynomials by QD-algorithm
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 3
SP - 210
EP - 219
AB - 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.
LA - eng
KW - numerical analysis
UR - http://eudml.org/doc/14594
ER -

References

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  1. Крылов В. И., Приближенное вычисление интегралов, Москва 1959. (1959) Zbl1047.90504
  2. G. Szegö, Orthogonal polynomials, AMS, N.Y. 1959. (1959) MR0106295
  3. H. Rutishauser, Der Quotienten-Differenzen-Algorithmus, Birkhäuser Verlag Basel/Stuttgart 1957. (1957) Zbl0077.11103MR0089499
  4. H. Rutishauser, On a modification of the QD-algorithm with Graeffe-type convergence, Information Processing 1962, North-Holland, Amsterdam 1963, pp. 93-96. (1962) Zbl0113.10702MR0251885
  5. J. Fiala, Řešení algebraických rovnic QD-algoritmem, Zpráva a program 7-07-04, VLD Praha, 1964. (1964) 
  6. Айзенштад В. С., Крылов В. И., МетелъскийА. С., Таблицы для численного преобразования Лапласа и вычисления интегралов вида ∫ 0 + ∞ x s e - x f ( x ) d x , АН БССР Минск 1962. (1962) 
  7. P. Rabinowitz, G. Weiss, Tables of Abscissas and weights for numerical evaluation of integrals of the form ∫ 0 + ∞ e - x x n f ( x ) d x , Math. Tables and Other Aids to Соmр. 13 (1959) 285-293. (1959) MR0107992
  8. Head, Wilson, Laguerre functions: Tables and properties, Proc. I.E.E., Part C, 103 (1956) 428. (1956) 
  9. H. Wall, Analytic theory of continued fractions, N.Y. 1948. (1948) Zbl0035.03601MR0025596

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