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On node distributions for interpolation and spectral methods


Author: N. S. Hoang
Journal: Math. Comp. 85 (2016), 667-692
MSC (2010): Primary 65D05; Secondary 41A05, 41A10
DOI: https://doi.org/10.1090/mcom/3018
Published electronically: September 23, 2015
MathSciNet review: 3434875
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Abstract: A scaled Chebyshev node distribution is studied in this paper. It is proved that the node distribution is optimal for interpolation in $ C_M^{s+1}[-1,1]$, the set of $ (s+1)$-time differentiable functions whose $ (s+1)$-th derivatives are bounded in absolute value by a constant $ M>0$. Node distributions for computing spectral differentiation matrices and integration matrices are proposed and studied. Numerical experiments have shown that the proposed node distributions can yield results of higher accuracy than those obtained by the most commonly used Chebyshev-Gauss-Lobatto node distribution.


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Additional Information

N. S. Hoang
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: nhoang@westga.edu

DOI: https://doi.org/10.1090/mcom/3018
Keywords: Interpolation, pseudospectral methods, node distributions, differentiation matrices, integration matrices, scaled Chebyshev nodes, Chebyshev nodes, Chebyshev-Gauss-Lobatto nodes.
Received by editor(s): August 5, 2013
Received by editor(s) in revised form: July 18, 2014
Published electronically: September 23, 2015
Article copyright: © Copyright 2015 American Mathematical Society