Note on error bounds for numerical integration
Abstract: A length functional was defined in a previous publication which associates a length scale r to every function analytic on a given interval. The ratio of r to the mean panel size for numerical integration on that interval was defined as the sketchability. Stronger error bounds are given here for interpolative integration schemes in terms of the sketchability. Since these are not least upper bounds we also present lower limits for the least upper bounds obtained from actual numerical integrations of specific sketchability. We find the gap between the bounds and their lower limits to be small enough to be ignored for most applications.
-  J. H. Hetherington, An error bound for quadratures, Math. Comp. 26 (1972), 695–698. MR 0331732, https://doi.org/10.1090/S0025-5718-1972-0331732-2
-  Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604
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Keywords: Newton-Cotes quadrature, Gaussian quadrature, quadrature error bounds
Article copyright: © Copyright 1973 American Mathematical Society