Existence of quadrature formulae with almost equal weights
Author:
K. Salkauskas
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
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Abstract | References | Similar Articles | Additional Information
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.
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- [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
- [3] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
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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
