Numerical Solution for the Extrapolation Problem of Analytic Functions
In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude...
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| Format: | Article |
| Language: | English |
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American Association for the Advancement of Science (AAAS)
2019-01-01
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| Series: | Research |
| Online Access: | http://dx.doi.org/10.34133/2019/3903187 |
| _version_ | 1797287519789776896 |
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| author | Nikolaos P. Bakas |
| author_facet | Nikolaos P. Bakas |
| author_sort | Nikolaos P. Bakas |
| collection | DOAJ |
| description | In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function’s direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases. |
| first_indexed | 2024-03-07T18:34:21Z |
| format | Article |
| id | doaj.art-ae70e56849d24e239f9d6b895787eebc |
| institution | Directory Open Access Journal |
| issn | 2639-5274 |
| language | English |
| last_indexed | 2024-03-07T18:34:21Z |
| publishDate | 2019-01-01 |
| publisher | American Association for the Advancement of Science (AAAS) |
| record_format | Article |
| series | Research |
| spelling | doaj.art-ae70e56849d24e239f9d6b895787eebc2024-03-02T05:26:29ZengAmerican Association for the Advancement of Science (AAAS)Research2639-52742019-01-01201910.34133/2019/3903187Numerical Solution for the Extrapolation Problem of Analytic FunctionsNikolaos P. Bakas0Intelligent Systems Lab & Civil Engineering Department, School of Architecture, Engineering, Land and Environmental Sciences, Neapolis University Pafos, 2 Danais Avenue, 8042 Paphos, CyprusIn this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function’s direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases.http://dx.doi.org/10.34133/2019/3903187 |
| spellingShingle | Nikolaos P. Bakas Numerical Solution for the Extrapolation Problem of Analytic Functions Research |
| title | Numerical Solution for the Extrapolation Problem of Analytic Functions |
| title_full | Numerical Solution for the Extrapolation Problem of Analytic Functions |
| title_fullStr | Numerical Solution for the Extrapolation Problem of Analytic Functions |
| title_full_unstemmed | Numerical Solution for the Extrapolation Problem of Analytic Functions |
| title_short | Numerical Solution for the Extrapolation Problem of Analytic Functions |
| title_sort | numerical solution for the extrapolation problem of analytic functions |
| url | http://dx.doi.org/10.34133/2019/3903187 |
| work_keys_str_mv | AT nikolaospbakas numericalsolutionfortheextrapolationproblemofanalyticfunctions |