Revisited Optimal Error Bounds for Interpolatory Integration Rules. (16th November 2016)

• Record Type: Journal Article
• Authors: Dubeau, François
• Other Names: Adjerid Slimane Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2016(2016)
• Publication Date: 2016-11-16
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2016/3170595
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor's expansion. These bounds depend on the regularity of the integrand. The method of integration by parts "backwards" to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.