On exponential convergence of Gegenbauer interpolation and spectral differentiation

Xie, Ziqing; Wang, Li-Lian; Zhao, Xiaodan

doi:10.1090/S0025-5718-2012-02645-7

On exponential convergence of Gegenbauer interpolation and spectral differentiation
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by Ziqing Xie, Li-Lian Wang and Xiaodan Zhao PDF

Math. Comp. 82 (2013), 1017-1036 Request permission

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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