Paper Info
Title
Superconvergence of Jacobi---Gauss-Type Spectral Interpolation
Abstract
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.
Year
DOI
Venue
2014
10.1007/s10915-013-9777-x
J. Sci. Comput.
Keywords
Field
DocType
rigorous error analysis,chebyshev-gauss-type spectral interpolation,superconvergence analysis,analytic function,superconvergence property,gauss-type spectral interpolation,siam j numer anal,interpolation error,superconvergence point,interpolation error bound,gauss-type interpolation
Gauss,Mathematical optimization,Interpolation error,Mathematical analysis,Analytic function,Interpolation,Superconvergence,Legendre polynomials,Rate of convergence,Exponential convergence,Mathematics
Journal
Volume
Issue
ISSN
59
3
1573-7691
Citations 
PageRank 
References 
5
0.47
12
Authors
3
Name
Order
Citations
PageRank
Li-Lian Wang136743.47
Xiaodan Zhao2548.84
Zhimin Zhang310716.72