The Akima's fitting method for quartic splines
For the Hermite type quartic spline interpolating on the partition knots and at the midpoint of each subinterval, we consider the estimation of the derivatives on the knots, and the values of these derivatives are obtained by constructing an algorithm of Akima's type. For computing the derivat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2022-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1278 |
| _version_ | 1797973461136572416 |
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| author | Alexandru Mihai Bica Diana Curilă (Popescu) |
| author_facet | Alexandru Mihai Bica Diana Curilă (Popescu) |
| author_sort | Alexandru Mihai Bica |
| collection | DOAJ |
| description |
For the Hermite type quartic spline interpolating on the partition knots and at the midpoint of each subinterval, we consider the estimation of the derivatives on the knots, and the values of these derivatives are obtained by constructing an algorithm of Akima's type. For computing the derivatives on endpoints are also considered alternatives that request optimal properties near the endpoints. The error estimate in the interpolation with this quartic spline is generally obtained in terms of the modulus of continuity. In the case of interpolating smooth functions, the corresponding error estimate reveal the maximal order of approximation O(h^3). A numerical experiment is presented for making the comparison between the Akima's cubic spline and the Akima's variant quartic spline having
deficiency 2 and natural endpoint conditions.
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| first_indexed | 2024-04-11T04:03:31Z |
| format | Article |
| id | doaj.art-ed35e3b27f7243c692fffd5d8aeac82f |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-11T04:03:31Z |
| publishDate | 2022-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-ed35e3b27f7243c692fffd5d8aeac82f2023-01-01T14:18:11ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2022-12-01512The Akima's fitting method for quartic splinesAlexandru Mihai Bica0Diana Curilă (Popescu)1University of Oradea, Department of Mathematics and Computer ScienceUniversity of Oradea, Department of Mathematics and Informatics For the Hermite type quartic spline interpolating on the partition knots and at the midpoint of each subinterval, we consider the estimation of the derivatives on the knots, and the values of these derivatives are obtained by constructing an algorithm of Akima's type. For computing the derivatives on endpoints are also considered alternatives that request optimal properties near the endpoints. The error estimate in the interpolation with this quartic spline is generally obtained in terms of the modulus of continuity. In the case of interpolating smooth functions, the corresponding error estimate reveal the maximal order of approximation O(h^3). A numerical experiment is presented for making the comparison between the Akima's cubic spline and the Akima's variant quartic spline having deficiency 2 and natural endpoint conditions. https://ictp.acad.ro/jnaat/journal/article/view/1278Quartic splinesAkima's fitting spline interpolation procedureerror estimates |
| spellingShingle | Alexandru Mihai Bica Diana Curilă (Popescu) The Akima's fitting method for quartic splines Journal of Numerical Analysis and Approximation Theory Quartic splines Akima's fitting spline interpolation procedure error estimates |
| title | The Akima's fitting method for quartic splines |
| title_full | The Akima's fitting method for quartic splines |
| title_fullStr | The Akima's fitting method for quartic splines |
| title_full_unstemmed | The Akima's fitting method for quartic splines |
| title_short | The Akima's fitting method for quartic splines |
| title_sort | akima s fitting method for quartic splines |
| topic | Quartic splines Akima's fitting spline interpolation procedure error estimates |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1278 |
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