Optimal Rational Approximations by the Modified Fourier Basis
We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise conver...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/1705409 |
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| author | Arnak V. Poghosyan Tigran K. Bakaryan |
| author_facet | Arnak V. Poghosyan Tigran K. Bakaryan |
| author_sort | Arnak V. Poghosyan |
| collection | DOAJ |
| description | We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis. |
| format | Article |
| id | doaj-art-d878e5c2de494f3cb4bd42627361b9d3 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d878e5c2de494f3cb4bd42627361b9d32025-08-20T02:20:57ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/17054091705409Optimal Rational Approximations by the Modified Fourier BasisArnak V. Poghosyan0Tigran K. Bakaryan1Institute of Mathematics, Armenian National Academy of Sciences, 24/5 Marshal Baghramyan Ave., 0019 Yerevan, ArmeniaInstitute of Mathematics, Armenian National Academy of Sciences, 24/5 Marshal Baghramyan Ave., 0019 Yerevan, ArmeniaWe consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis.http://dx.doi.org/10.1155/2018/1705409 |
| spellingShingle | Arnak V. Poghosyan Tigran K. Bakaryan Optimal Rational Approximations by the Modified Fourier Basis Abstract and Applied Analysis |
| title | Optimal Rational Approximations by the Modified Fourier Basis |
| title_full | Optimal Rational Approximations by the Modified Fourier Basis |
| title_fullStr | Optimal Rational Approximations by the Modified Fourier Basis |
| title_full_unstemmed | Optimal Rational Approximations by the Modified Fourier Basis |
| title_short | Optimal Rational Approximations by the Modified Fourier Basis |
| title_sort | optimal rational approximations by the modified fourier basis |
| url | http://dx.doi.org/10.1155/2018/1705409 |
| work_keys_str_mv | AT arnakvpoghosyan optimalrationalapproximationsbythemodifiedfourierbasis AT tigrankbakaryan optimalrationalapproximationsbythemodifiedfourierbasis |