Article
Keywords:
numerical analysis
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.
References:
[1] Крылов В. И.:
Приближенное вычисление интегралов. Москва 1959.
Zbl 1047.90504
[2] G. Szegö:
Orthogonal polynomials. AMS, N.Y. 1959.
MR 0106295
[3] H. Rutishauser:
Der Quotienten-Differenzen-Algorithmus. Birkhäuser Verlag Basel/Stuttgart 1957.
MR 0089499 |
Zbl 0077.11103
[4] H. Rutishauser:
On a modification of the QD-algorithm with Graeffe-type convergence. Information Processing 1962, North-Holland, Amsterdam 1963, pp. 93-96.
MR 0251885 |
Zbl 0113.10702
[5] J. Fiala: Řešení algebraických rovnic QD-algoritmem. Zpráva a program 7-07-04, VLD Praha, 1964.
[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.
[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
[8] Head, Wilson: Laguerre functions: Tables and properties. Proc. I.E.E., Part C, 103 (1956) 428.