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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Monotonicity of quadrature approximations


Author: D. J. Newman
Journal: Proc. Amer. Math. Soc. 42 (1974), 251-257
MSC: Primary 41A55; Secondary 65D30
MathSciNet review: 0330865
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Abstract: For the general quadrature rules of Newton-Cotes we show that the convergence is monotone for the appropriate class of functions. Included are the well-known trapezoidal and Simpson rules.


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

  • [1] L. M. Milne-Thompson, Calculus of finite differences, Macmillan, New York, 1933.
  • [2] J. Molluzo, Doctoral Thesis, Yeshiva University, 1972 (unpublished).
  • [3] G. Szegö and P. Turán, On the monotone convergence of certain Riemann sums, Publ. Math. Debrecen 8 (1961), 326–335. MR 0137818 (25 #1267)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0330865-8
PII: S 0002-9939(1974)0330865-8
Keywords: Monotonicity, quadrature
Article copyright: © Copyright 1974 American Mathematical Society