On Corrected Quadrature Rules and Optimal Error Bounds
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 cont...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/461918 |
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| _version_ | 1832568305082171392 |
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| author | François Dubeau |
| author_facet | François Dubeau |
| author_sort | François Dubeau |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9c584bf8e4d84b5884d2e020e6e68a99 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9c584bf8e4d84b5884d2e020e6e68a992025-02-03T00:59:22ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/461918461918On Corrected Quadrature Rules and Optimal Error BoundsFrançois Dubeau0Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, 2500 boulevard de l’Université, Sherbrooke, QC, J1K 2R1, CanadaWe 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.http://dx.doi.org/10.1155/2015/461918 |
| spellingShingle | François Dubeau On Corrected Quadrature Rules and Optimal Error Bounds Abstract and Applied Analysis |
| title | On Corrected Quadrature Rules and Optimal Error Bounds |
| title_full | On Corrected Quadrature Rules and Optimal Error Bounds |
| title_fullStr | On Corrected Quadrature Rules and Optimal Error Bounds |
| title_full_unstemmed | On Corrected Quadrature Rules and Optimal Error Bounds |
| title_short | On Corrected Quadrature Rules and Optimal Error Bounds |
| title_sort | on corrected quadrature rules and optimal error bounds |
| url | http://dx.doi.org/10.1155/2015/461918 |
| work_keys_str_mv | AT francoisdubeau oncorrectedquadraturerulesandoptimalerrorbounds |