Accurate computation of weights in classical Gauss-Christoffel quadrature rules

Journal of Computational Physics

Volumn 129, Issue 2, 1996, Pages 406-430

  Yakimiw, E ^a  

^a Recherche en Prévision Numérique environnementale Environnement Canada   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; GAUSSIAN DISTRIBUTION;

'CURRENT; ACCURATE COMPUTATIONS; ALGEBRAIC EXPRESSION; GAUSSIAN QUADRATURES; HIGH-ORDER; HIGHER-ORDER; NODE LOCATION; QUADRATURE RULES; QUADRATURE WEIGHTS; SMALL PERTURBATIONS;

ITERATIVE METHODS;

EID: 0030524993     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0258     Document Type: Article

References (22)

1. 1. F. B. Hildebrand, Introduction to Numerical Analysis, 2nd ed. (McGraw-Hill, New York, 1974).
2. 2. W. Gautschi, "A Survey of Gauss-Christoffel Quadrature Formulae," in E. B. Christoffel. The Influence of His Work in Mathematics and the Physical Sciences, edited by P. L. Butzer and F. Feher (Birkhaüser, Basel, 1981), p. 72.
3. 3. P. Davis and Rabinowitz P, Methods of Numerical Integration 2nd ed. (Academic Press, San Diego, 1984).
4. 4. W. Gautschi, Math. Comput. 57, 309 (1991).
5. 5. G. V. Milovanovic, "Summation of Series and Gaussian Quadrature," in International Series of Numerical Mathematics, Vol. 119, edited by R. V. M. Zahar (Birkhaüser, Basel, 1994), p. 459.
6. 6. G. Mastroianni and G. Monegato, "Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas," in E. B. Christoffel. The Influence of His Work in Mathematics and the Physical Sciences, edited by P. L. Butzer and F. Feher (Birkhaüser, Basel, 1981), p. 421.
7. 7. W. Gautschi and S. Li, J. Comput. Appl. Math. 34, 343 (1991).
8. 8. W. Gautschi, Math. Comput. 22, 251 (1968).
9. 9. F. G. Lether, J. Comput. Appl. Math. 4, 47 (1978).
10. 10. T. Nehrkorn, Mon. Weather Rev. 118, 2248 (1990).
11. 11. E. Yakimiw, "On the Accurate Computation of the Weights in Gaussian Quadrature," in Proceedings, Third Annual Conference of the CFD Society of Canada, 25-27 June 1995, Banff, Canada, Vol. 1, p. 121 edited by P. A. Thibault and D. M. Bergeron (CFD Soc., Canada, 1995).
12. 12. H. Ritchie, C. Temperton, A. Simmons, M. Hortal, T. Davies, D. Dent, and M. Hamrud, Mon. Weather Rev. 123, 489 (1995).
13. 13. G. H. Golub and J. H. Welsh, Math. Comput. 23, 221 (1969).
14. 14. A. M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, 3rd ed. (Academic Press, New York, 1973).
15. 15. J. F. Traub, Iterative Methods for the Solution of Equations (Prentice-Hall, Englewood Cliffs, NJ, 1964).
16. 16. J. H. Wilkinson and C. Reinsch, Linear Algebra in Handbook for Automatic Computation, Vol. 2 (Springer-Verlag, New York, 1971).
17. 17. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1969).
18. 18. L. Fox and D. F. Mayers, Computing Methods for Scientists and Engineers (Clarendon Press, Oxford, 1968).
19. 19. J. Gerlach, SIAM Rev. 36, 272 (1994).
20. 20. M. Branders, R. Piessens, and M. De Meue, J. Comput. Phys. 42, 403 (1981).
21. 21. A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas (Prentice-Hall, Englewood Cliffs, NJ, 1966).
22. 22. E. Yakimiw, "Second-Order Correction to the Weight Formulas in Gaussian Quadrature," in Proceedings of the Sixth International Symposium on Computational Fluid Dynamics, Sept. 4-8, 1995, Lake Tahoe, NV, Vol. 3, p. 1399, edited by M. Hafez (University of California, Davis, 1995).