Existence of quadrature formulae with almost equal weights
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- by K. Salkauskas PDF
- Math. Comp. 25 (1971), 105-109 Request permission
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
- Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Company, 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, Publication of the Mathematics Research Center, U.S. Army, the University of Wisconsin, no. 1, University of Wisconsin Press, Madison, Wis., 1959, pp. 3–10. Edited by R. E. Langer. MR 0100956
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 105-109
- MSC: Primary 65.55
- DOI: https://doi.org/10.1090/S0025-5718-1971-0290570-9
- MathSciNet review: 0290570