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Existence of quadrature formulae with almost equal weights


Author: K. Salkauskas
Journal: Math. Comp. 25 (1971), 105-109
MSC: Primary 65.55
MathSciNet review: 0290570
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Abstract: The condition that an interpolatory quadrature formula on n nodes have degree of precision at least n and positive weights defines a homeomorphism between the sets of admissible nodes and weights of such formulae for each n. This is used to prove that the only formulae having "almost equal" weights are the Chebyshev formulae.


References [Enhancements On Off] (What's this?)

  • [1] Vladimir Ivanovich Krylov, Approximate calculation of integrals, Translated by Arthur H. Stroud, The Macmillan Co., New York-London, 1962, 1962. MR 0144464
  • [2] Alexander M. Ostrowski, On trends and problems in numerical approximation, On numerical approximation. Proceedings of a Symposium, Madison, April 21–23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, pp. 3–10. MR 0100956
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0290570-9
Keywords: Chebyshev quadrature, almost equally weighted quadrature
Article copyright: © Copyright 1971 American Mathematical Society