About a dubious proof of a correct result about closed Newton Cotes error formulas
In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [a,b].\left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-11-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2023-0150 |
| _version_ | 1797435639474421760 |
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| author | López David J. Padilla Jose A. Ruiz Juan Tapia Carlos Trillo Juan C. |
| author_facet | López David J. Padilla Jose A. Ruiz Juan Tapia Carlos Trillo Juan C. |
| author_sort | López David J. |
| collection | DOAJ |
| description | In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [a,b].\left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel. |
| first_indexed | 2024-03-09T10:51:08Z |
| format | Article |
| id | doaj.art-1d01bbcbd2aa4d4eb167271ec737587d |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-09T10:51:08Z |
| publishDate | 2023-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-1d01bbcbd2aa4d4eb167271ec737587d2023-12-01T07:18:44ZengDe GruyterOpen Mathematics2391-54552023-11-012113840385610.1515/math-2023-0150About a dubious proof of a correct result about closed Newton Cotes error formulasLópez David J.0Padilla Jose A.1Ruiz Juan2Tapia Carlos3Trillo Juan C.4Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SpainDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SpainDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SpainDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SpainDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SpainIn this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [a,b].\left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.https://doi.org/10.1515/math-2023-0150newton cotesclosedintegrationerror formulassimpson 3/841a0541a5565d3065d32 |
| spellingShingle | López David J. Padilla Jose A. Ruiz Juan Tapia Carlos Trillo Juan C. About a dubious proof of a correct result about closed Newton Cotes error formulas Open Mathematics newton cotes closed integration error formulas simpson 3/8 41a05 41a55 65d30 65d32 |
| title | About a dubious proof of a correct result about closed Newton Cotes error formulas |
| title_full | About a dubious proof of a correct result about closed Newton Cotes error formulas |
| title_fullStr | About a dubious proof of a correct result about closed Newton Cotes error formulas |
| title_full_unstemmed | About a dubious proof of a correct result about closed Newton Cotes error formulas |
| title_short | About a dubious proof of a correct result about closed Newton Cotes error formulas |
| title_sort | about a dubious proof of a correct result about closed newton cotes error formulas |
| topic | newton cotes closed integration error formulas simpson 3/8 41a05 41a55 65d30 65d32 |
| url | https://doi.org/10.1515/math-2023-0150 |
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