Adaptive Integration of Convex Functions of One Real Variable
We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.
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| Format: | Article |
| Language: | English |
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Sciendo
2024-03-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2023-0028 |
| _version_ | 1797229592327487488 |
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| author | Wąsowicz Szymon |
| author_facet | Wąsowicz Szymon |
| author_sort | Wąsowicz Szymon |
| collection | DOAJ |
| description | We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown. |
| first_indexed | 2024-04-24T15:15:02Z |
| format | Article |
| id | doaj.art-86662c761fb74cb09bd80a276a3c5fc6 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-04-24T15:15:02Z |
| publishDate | 2024-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-86662c761fb74cb09bd80a276a3c5fc62024-04-02T09:28:47ZengSciendoAnnales Mathematicae Silesianae2391-42382024-03-0138112013310.2478/amsil-2023-0028Adaptive Integration of Convex Functions of One Real VariableWąsowicz Szymon01Department of Mathematics, University of Bielsko–Biala, Willowa 2, 43–309Bielsko–Biała, PolandWe present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.https://doi.org/10.2478/amsil-2023-0028adaptive integrationconvex functionhermite–hadamard inequalityquadraturemidpoint ruletrapezoid rule41a5565d3065d3226a5126d15 |
| spellingShingle | Wąsowicz Szymon Adaptive Integration of Convex Functions of One Real Variable Annales Mathematicae Silesianae adaptive integration convex function hermite–hadamard inequality quadrature midpoint rule trapezoid rule 41a55 65d30 65d32 26a51 26d15 |
| title | Adaptive Integration of Convex Functions of One Real Variable |
| title_full | Adaptive Integration of Convex Functions of One Real Variable |
| title_fullStr | Adaptive Integration of Convex Functions of One Real Variable |
| title_full_unstemmed | Adaptive Integration of Convex Functions of One Real Variable |
| title_short | Adaptive Integration of Convex Functions of One Real Variable |
| title_sort | adaptive integration of convex functions of one real variable |
| topic | adaptive integration convex function hermite–hadamard inequality quadrature midpoint rule trapezoid rule 41a55 65d30 65d32 26a51 26d15 |
| url | https://doi.org/10.2478/amsil-2023-0028 |
| work_keys_str_mv | AT wasowiczszymon adaptiveintegrationofconvexfunctionsofonerealvariable |