Geodesic
Zeroes of orthogonal polynomials by QD-algorithm
Applications of Mathematics, Tome 14 (1969) no. 3, pp. 210-219
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1969.103226
Classification : 65.50
Keywords: numerical analysis 
@article{10_21136_AM_1969_103226,
     author = {Fiala, Ji\v{r}{\'\i}},
     title = {Zeroes of orthogonal polynomials by {QD-algorithm}},
     journal = {Applications of Mathematics},
     pages = {210--219},
     year = {1969},
     volume = {14},
     number = {3},
     doi = {10.21136/AM.1969.103226},
     mrnumber = {0248976},
     zbl = {0194.18304},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103226/}
}
TY  - JOUR
AU  - Fiala, Jiří
TI  - Zeroes of orthogonal polynomials by QD-algorithm
JO  - Applications of Mathematics
PY  - 1969
SP  - 210
EP  - 219
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103226/
DO  - 10.21136/AM.1969.103226
LA  - en
ID  - 10_21136_AM_1969_103226
ER  - 
%0 Journal Article
%A Fiala, Jiří
%T Zeroes of orthogonal polynomials by QD-algorithm
%J Applications of Mathematics
%D 1969
%P 210-219
%V 14
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103226/
%R 10.21136/AM.1969.103226
%G en
%F 10_21136_AM_1969_103226
Fiala, Jiří. Zeroes of orthogonal polynomials by QD-algorithm. Applications of Mathematics, Tome 14 (1969) no. 3, pp. 210-219. doi: 10.21136/AM.1969.103226

[1] Крылов В. И.: Приближенное вычисление интегралов. Москва 1959. | Zbl

[2] G. Szegö: Orthogonal polynomials. AMS, N.Y. 1959. | MR

[3] H. Rutishauser: Der Quotienten-Differenzen-Algorithmus. Birkhäuser Verlag Basel/Stuttgart 1957. | MR | Zbl

[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 | Zbl

[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

[8] Head, Wilson: Laguerre functions: Tables and properties. Proc. I.E.E., Part C, 103 (1956) 428.

[9] H. Wall: Analytic theory of continued fractions. N.Y. 1948. | MR | Zbl

Cité par Sources :