A Rational Interpolation Scheme with Superpolynomial Rate of Convergence
The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor seri...
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| Formato: | Artigo |
| Idioma: | en_US |
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Society for Industrial and Applied Mathematics
2010
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| Acesso em linha: | http://hdl.handle.net/1721.1/57504 https://orcid.org/0000-0001-9669-2563 |
| _version_ | 1826215490192670720 |
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| author | Wang, Qiqi Moin, Parviz Iaccarino, Gianluca |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi Moin, Parviz Iaccarino, Gianluca |
| author_sort | Wang, Qiqi |
| collection | MIT |
| description | The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor series, and the approximation error as a combination of the derivatives of the target function. A weighted sum of the square of the coefficient of each derivative term in the approximation error is minimized to obtain the interpolation approximation. The resulting approximation function is a high-order rational function with no poles. When measurement errors are absent, the interpolation approximation converges to the target function faster than any polynomial rate of convergence. |
| first_indexed | 2024-09-23T16:31:41Z |
| format | Article |
| id | mit-1721.1/57504 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:31:41Z |
| publishDate | 2010 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/575042022-10-02T08:13:37Z A Rational Interpolation Scheme with Superpolynomial Rate of Convergence Wang, Qiqi Moin, Parviz Iaccarino, Gianluca Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Wang, Qiqi Wang, Qiqi rational interpolation nonlinear regression function approximation approximation order The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor series, and the approximation error as a combination of the derivatives of the target function. A weighted sum of the square of the coefficient of each derivative term in the approximation error is minimized to obtain the interpolation approximation. The resulting approximation function is a high-order rational function with no poles. When measurement errors are absent, the interpolation approximation converges to the target function faster than any polynomial rate of convergence. 2010-08-17T14:12:59Z 2010-08-17T14:12:59Z 2010-01 2008-11 Article http://purl.org/eprint/type/JournalArticle 0036-1429 1095-7170 http://hdl.handle.net/1721.1/57504 Wang, Qiqi, Parviz Moin, and Gianluca Iaccarino. “A Rational Interpolation Scheme with Superpolynomial Rate of Convergence.” SIAM Journal on Numerical Analysis 47.6 (2010): 4073-4097. © 2010 Society for Industrial and Applied Mathematics https://orcid.org/0000-0001-9669-2563 en_US http://dx.doi.org/10.1137/080741574 SIAM Journal on Numerical Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | rational interpolation nonlinear regression function approximation approximation order Wang, Qiqi Moin, Parviz Iaccarino, Gianluca A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title | A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title_full | A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title_fullStr | A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title_full_unstemmed | A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title_short | A Rational Interpolation Scheme with Superpolynomial Rate of Convergence |
| title_sort | rational interpolation scheme with superpolynomial rate of convergence |
| topic | rational interpolation nonlinear regression function approximation approximation order |
| url | http://hdl.handle.net/1721.1/57504 https://orcid.org/0000-0001-9669-2563 |
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