On the computation of the Gauss-Legendre quadrature formula with a given precision

Journal of Computational and Applied Mathematics

Volumn 112, Issue 1-2, 1999, Pages 253-267

  Petras, Knut ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

33C45; 65D32; 65H05; Gaussian quadrature; Legendre polynomials; Newton method; Root finding

Indexed keywords

APPROXIMATION THEORY; ITERATIVE METHODS; POLES AND ZEROS;

GAUSS-LEGENDRE QUADRATURE FORMULA; NEWTON METHOD;

POLYNOMIALS;

EID: 0033343682     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00225-3     Document Type: Article

References (13)

1. H. Brass, Quadraturverfahren, Vandenhoeck & Ruprecht, Göttingen, 1977.
2. P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, London, 1984.
3. Förster K.-J., Petras K. On estimates for the weights in Gaussian quadrature in the ultraspherical case. Math. Comp. 55:1990;243-264.
4. Förster K.-J., Petras K. On the zeros of ultraspherical polynomials and Bessel functions. IMACS Ann. Comput. Appl. Math. 9:1991;257-262.
5. Förster K.-J., Petras K. Inequalities for the zeros of ultraspherical polynomials and Bessel functions. Z. Angew. Math. Mech. 73:1993;232-236.
6. Gatteschi L. New inequalities for the zeros of Jacobi polynomials. SIAM J. Math. Anal. 18:1987;1549-1562.
7. W. Gautschi, A survey of Gauss-Christoffel quadrature formulae, in: P.L. Butzer, F. Fehér (Eds.), E.B. Christoffel, Birkhäuser, Basel, 1981, pp. 72-147.
8. Lether F.G. On the construction of Gauss-Legendre quadrature rules. J. Comput. Appl. Math. 4:1978;47-52.
9. n(x) and Gauss-Legendre quadrature J. Comput. Appl. Math. 59:1995;245-252.
10. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C , 2nd Edition, Cambridge University Press, Cambridge, 1992.
11. R. Schaback, H. Werner, Numerische Mathematik, 4th Edition, Springer, Berlin, 1992.
12. G. Schmeisser, H. Schirmeier, Praktische Mathematik, de Gruyter, Berlin, 1976.
13. G. Szegö, Orthogonal Polynomials, AMS, Providence, RI, 1939.