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On exponential convergence of Gegenbauer interpolation and spectral differentiation


Authors: Ziqing Xie, Li-Lian Wang and Xiaodan Zhao
Journal: Math. Comp. 82 (2013), 1017-1036
MSC (2010): Primary 65N35, 65E05, 65M70, 41A05, 41A10, 41A25
DOI: https://doi.org/10.1090/S0025-5718-2012-02645-7
Published electronically: August 21, 2012
MathSciNet review: 3008847
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Abstract: This paper is devoted to a rigorous analysis of exponential convergence of polynomial interpolation and spectral differentiation based on the Gegenbauer-Gauss and Gegenbauer-Gauss-Lobatto points, when the underlying function is analytic on and within an ellipse. Sharp error estimates in the maximum norm are derived.


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Additional Information

Ziqing Xie
Affiliation: School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, China — and — Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China
Email: ziqingxie@yahoo.com.cn

Li-Lian Wang
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Email: lilian@ntu.edu.sg

Xiaodan Zhao
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Email: zhao0122@e.ntu.edu.sg

DOI: https://doi.org/10.1090/S0025-5718-2012-02645-7
Keywords: Bernstein ellipse, exponential accuracy, Gegenbauer polynomials, Gegenbauer Gauss-type interpolation and quadrature, spectral differentiation, maximum error estimates
Received by editor(s): January 12, 2011
Received by editor(s) in revised form: August 18, 2011, and October 9, 2011
Published electronically: August 21, 2012
Additional Notes: The research of the first author is partially supported by the NSFC (11171104, 10871066) and the Science and Technology Grant of Guizhou Province (LKS[2010]05)
The research of the second and third authors is partially supported by Singapore AcRF Tier 1 Grant RG58/08
Article copyright: © Copyright 2012 American Mathematical Society

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