| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2008-05-20T17:45:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103226 |
| . |
| 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 |
| . |
