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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?)

  • Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Co., New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR 0144464
  • 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
  • Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493

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Keywords: Chebyshev quadrature, almost equally weighted quadrature
Article copyright: © Copyright 1971 American Mathematical Society