On corrected quadrature rules and optimal error bounds
type: Item
instance of: scholarly article
title: On corrected quadrature rules and optimal error bounds
zbMATH Open document ID: 1433.65030
DOI: 10.1155/2015/461918
author: F. Dubeau
published in: Abstract and Applied Analysis
publication date: 2018-08-29T00:00:00Z
review text: Summary: We present an analysis of corrected quadrature rules based on the method of undetermined coefficients and its associated degree of accuracy. The correcting terms use weighted values of the first derivative of the function at the endpoint of the subinterval in such a way that the composite rules contain only two new values. Using Taylor's expansions and Peano's kernels we obtain best truncation error bounds which depend on the regularity of the function and the weight parameter. We can minimize the bounds with respect to the parameter, and we can find the best parameter value to increase the order of the error bounds or, equivalently, the degree of accuracy of the rule.
Mathematics Subject Classification ID: 65D30
zbMATH DE Number: 6929049
Wikidata QID: Q59101641
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/461918
OpenAlex ID: W1930001340
cites work: Q3323133
cites work: Error estimates for some composite corrected quadrature rules
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description: scientific article; zbMATH DE number 6929049