Revisited Optimal Error Bounds for Interpolatory Integration Rules | Zendy

François Dubeau | Zendy

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Revisited Optimal Error Bounds for Interpolatory Integration Rules

Author(s) -

François Dubeau

Publication year - 2016

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2016/3170595

Subject(s) - numerical integration , quadrature (astronomy) , peano axioms , mathematics , taylor series , integration by parts , interval (graph theory) , term (time) , error analysis , mathematical optimization , calculus (dental) , algorithm , mathematical analysis , combinatorics , medicine , dentistry , physics , electrical engineering , quantum mechanics , engineering

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

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