Generalized Kronrod Patterson type imbedded quadratures
Elhay, Sylvan ; Kautský, Jaroslav
Applications of Mathematics, Tome 37 (1992), p. 81-103 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.

Publié le : 1992-01-01
Classification:  41A55,  65D30,  65D32,  65F15 
@article{104494,
     author = {Sylvan Elhay and Jaroslav Kautsk\'y},
     title = {Generalized Kronrod Patterson type imbedded quadratures},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {81-103},
     zbl = {0754.65025},
     mrnumber = {1149160},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104494}
}

Elhay, Sylvan; Kautský, Jaroslav. Generalized Kronrod Patterson type imbedded quadratures. Applications of Mathematics, Tome 37 (1992) pp. 81-103. http://gdmltest.u-ga.fr/item/104494/

S. Elhay; J. Kautsky A method for computing quadratures of the Kronrod-Patterson type, Australian Computer Science Communications 6 (1) (1984), 15.1-15.8. (1984)

G. H. Golub; J. Kautsky Calculation of Gauss quadratures with multiple free and fixed knots, Numer. Math. 41 (1983), 147-163. (1983) | MR 0703119 | Zbl 0525.65010

D. K. Kahaner J. Waldvogel; And L. W. Fullerton Addition of points to Gauss-Laguerre quadrature formulae, SIAM J. Sci. Stat. Comput. 5 (1984), 42-55. (1984) | MR 0731880

J. Kautsky; S. Elhay Gauss quadratures and Jacobi matrices for weight functions not of one sign, Math. Соmр. 43 (168) (1984), 543-550. (1984) | MR 0758201 | Zbl 0556.65012

A. S. Kronrod Nodes and weights for quadrature formulae. Sixteen place tables, Nauka, Moscow; English translation, Consultants Bureau, New York. | MR 0183116

G. Monegato Stieltjes polynomials, and related quadrature rules, SIAM Review 24(2) (1982), 137-158. (1982) | Article | MR 0652464 | Zbl 0494.33010

T. N. L. Patterson The optimal addition of points to quadrature formulae, Math. Соmр. 22 (1968), 847-856. (1968) | MR 0242370

R. Piessens; M. Branders A note on the optimal addition of abscissae to quadrature formulae of the Gauss-Lobatto type, Math. Соmр. 28 (1974), 135-139. (1974) | MR 0343552

P. Turan On the theory of mechanical quadrature, Acta. Sci. Math. (Szeged) 12 (1950), 30-37. (1950) | MR 0036797