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Interpolatory product integration for Riemann-integrable functions

Published online by Cambridge University Press:  17 February 2009

Philip Rabinowitz  and
William E. Smith
Philip Rabinowitz
Affiliation:
Department of Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel.
William E. Smith
Affiliation:
Department of Applied Mathematics, University of New South Wales, P. O. Box 1, Kensington, N.S.W. 2033, Australia.
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Abstract

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Conditions are fround for the convergence of intepolatory product integration rules and the corresponding companion rules for the class of Riemann-integrable functions. These condtions are used to prove convergence for several classes of rules based on sets of zeros of orthogonal polynomials possibly augmented by one both of the endpoints of the integration interval.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 2 , October 1987 , pp. 195 - 202
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Davis, P. J. and Rabinowita, P., Methods of numerical integration, 2nd Edition (Academic Press, New York, 1984).Google Scholar
[2]Rabinowitz, P., “The convergence of interpolatoiy product integration rules”. BIT 26 (1986), 131–134.CrossRefGoogle Scholar
[3]Rabinowitz, P., “On the convergence of interpolatoay product integration rules based on Gauss, Radau and Lobatto points”, Israel J. Math. 56 (1986) 66–74.CrossRefGoogle Scholar
[4]Sloan, I. H., “On the numerical evaluation of singular integrals”. BIT 18 (1978) 91–102.CrossRefGoogle Scholar
[5]Sloan, I. H. and Smith, W. B., ”Properties of interpolatory product integration rules”, SIAM J. Numer. Anal. 19 (1982) 427–442.CrossRefGoogle Scholar
[6]Smith, W. B., “Erdös-Turán mean convergence for Lagrange interpolation at Lobatto points”, Bull. Austral. Math. Soc. 34 (1986) 375–381.CrossRefGoogle Scholar