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...

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Main Authors: Wang, Li-Lian, Zhao, Xiaodan, Zhang, Zhimin
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2014
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Online Access:https://hdl.handle.net/10356/104666
http://hdl.handle.net/10220/20264
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Physics
spellingShingle DRNTU::Science::Physics
Wang, Li-Lian
Zhao, Xiaodan
Zhang, Zhimin
Superconvergence of Jacobi Gauss type spectral interpolation
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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Wang, Li-Lian
Zhao, Xiaodan
Zhang, Zhimin
format Article
author Wang, Li-Lian
Zhao, Xiaodan
Zhang, Zhimin
author_sort Wang, Li-Lian
title Superconvergence of Jacobi Gauss type spectral interpolation
title_short 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_sort superconvergence of jacobi gauss type spectral interpolation
publishDate 2014
url https://hdl.handle.net/10356/104666
http://hdl.handle.net/10220/20264
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