NDLI: Superconvergence of Jacobi–Gauss-Type Spectral Interpolation

Content Provider	Springer Nature Link
Author	Wang, Li Lian Zhao, Xiaodan Zhang, Zhimin
Copyright Year	2013
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.
Starting Page	667
Ending Page	687
Page Count	21
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	59
Issue Number	3
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2013-09-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Superconvergence points Jacobi–Gauss Jacobi–Gauss–Radau and Jacobi–Gauss–Lobatto interpolations Analytic functions Bernstein ellipse Exponential convergence Error remainder Spectral, collocation and related methods Numerical methods in complex analysis Interpolation Approximation by polynomials Rate of convergence, degree of approximation Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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