Abstract
Conditions are given for the convergence of product integration rules based on the zeros of orthogonal polynomials associated with a generalized smooth Jacobi weight, possibly augmented by one or both endpoints.
Similar content being viewed by others
References
P. J. Davis and P. Rabinowitz,Methods of Numerical Integration, Second Edition, Academic Press, New York, 1984.
D. Elliott and D. F. Paget,Product-integration rules and their convergence, BIT 16 (1976) 32–40.
D. Elliott and D. F. Paget,The convergence of product integration rules, BIT 18 (1978) 137–141.
P. Nevai,Mean convergence of Lagrange interpolation. III, Trans. Amer. Math. Soc. 282 (1984) 669–698.
I. H. Sloan,On the numerical evaluation of singular integrals, BIT 18 (1978) 91–102.
I. H. Sloan and W. E. Smith,Product-integration with the Clenshaw-Curtis and related points. Convergence properties, Numer. Math. 30 (1978) 415–428.
I. H. Sloan and W. E. Smith,Properties of interpolatory product integration rules, SIAM J. Numer. Anal. 19 (1982) 427–442.
W. E. Smith and I. H. Sloan,Product-integration rules based on the zeros of Jacobi polynomials, SIAM J. Numer. Anal. 17 (1980) 1–13.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rabinowitz, P. The convergence of interpolatory product integration rules. BIT 26, 131–134 (1986). https://doi.org/10.1007/BF01939370
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01939370