Superconvergence of Jacobi Gauss type spectral interpolation
In this paper, we extend the study of superconvergence properties of Chebyshev-Gauss-type spectral interpolation in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to general Jacobi–Gauss-type interpolation. We follow the same principle as in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to identi...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Online Access: | https://hdl.handle.net/10356/104666 http://hdl.handle.net/10220/20264 |
| _version_ | 1811692143535718400 |
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| author | Wang, Li-Lian Zhao, Xiaodan Zhang, Zhimin |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Wang, Li-Lian Zhao, Xiaodan Zhang, Zhimin |
| author_sort | Wang, Li-Lian |
| collection | NTU |
| description | In this paper, we extend the study of superconvergence properties of Chebyshev-Gauss-type spectral interpolation in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to general Jacobi–Gauss-type interpolation. We follow the same principle as in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to identify superconvergence points from interpolating analytic functions, but rigorous error analysis turns out much more involved even for the Legendre case. We address the implication of this study to functions with limited regularity, that is, at superconvergence points of interpolating analytic functions, the leading term of the interpolation error vanishes, but there is no gain in order of convergence, which is in distinctive contrast with analytic functions. We provide a general framework for exponential convergence and superconvergence analysis. We also obtain interpolation error bounds for Jacobi–Gauss-type interpolation, and explicitly characterize the dependence of the underlying parameters and constants, whenever possible. Moreover, we provide illustrative numerical examples to show tightness of the bounds. |
| first_indexed | 2024-10-01T06:31:06Z |
| format | Journal Article |
| id | ntu-10356/104666 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:31:06Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1046662023-02-28T19:37:54Z Superconvergence of Jacobi Gauss type spectral interpolation Wang, Li-Lian Zhao, Xiaodan Zhang, Zhimin School of Physical and Mathematical Sciences DRNTU::Science::Physics In this paper, we extend the study of superconvergence properties of Chebyshev-Gauss-type spectral interpolation in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to general Jacobi–Gauss-type interpolation. We follow the same principle as in Zhang (SIAM J Numer Anal 50(5):2966–2985, 2012) to identify superconvergence points from interpolating analytic functions, but rigorous error analysis turns out much more involved even for the Legendre case. We address the implication of this study to functions with limited regularity, that is, at superconvergence points of interpolating analytic functions, the leading term of the interpolation error vanishes, but there is no gain in order of convergence, which is in distinctive contrast with analytic functions. We provide a general framework for exponential convergence and superconvergence analysis. We also obtain interpolation error bounds for Jacobi–Gauss-type interpolation, and explicitly characterize the dependence of the underlying parameters and constants, whenever possible. Moreover, we provide illustrative numerical examples to show tightness of the bounds. Accepted version 2014-08-06T08:38:04Z 2019-12-06T21:37:15Z 2014-08-06T08:38:04Z 2019-12-06T21:37:15Z 2014 2014 Journal Article Wang, L. L., Zhao, X., & Zhang, Z. (2014). Superconvergence of Jacobi–Gauss-Type Spectral Interpolation. Journal of Scientific Computing, 59(3), 667-687. 0885-7474 https://hdl.handle.net/10356/104666 http://hdl.handle.net/10220/20264 10.1007/s10915-013-9777-x en Journal of scientific computing © 2013 Springer Science+Business Media New York. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Scientific Computing, Springer Science+Business Media New York. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10915-013-9777-x]. 8 p. application/pdf |
| spellingShingle | DRNTU::Science::Physics Wang, Li-Lian Zhao, Xiaodan Zhang, Zhimin Superconvergence of Jacobi Gauss type spectral interpolation |
| title | Superconvergence of Jacobi Gauss type spectral interpolation |
| title_full | Superconvergence of Jacobi Gauss type spectral interpolation |
| title_fullStr | Superconvergence of Jacobi Gauss type spectral interpolation |
| title_full_unstemmed | Superconvergence of Jacobi Gauss type spectral interpolation |
| title_short | Superconvergence of Jacobi Gauss type spectral interpolation |
| title_sort | superconvergence of jacobi gauss type spectral interpolation |
| topic | DRNTU::Science::Physics |
| url | https://hdl.handle.net/10356/104666 http://hdl.handle.net/10220/20264 |
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