Superconvergence of Jacobi-Gauss-Type Spectral Interpolation

نویسندگان

  • Li-Lian Wang
  • Xiaodan Zhao
  • Zhimin Zhang
چکیده

In this paper, we extend the study of superconvergence properties of ChebyshevGauss-type spectral interpolation in [24, SINUM,Vol. 50, 2012] to general Jacobi-Gauss-type interpolation. We follow the same principle as in [24] 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-Gausstype 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.

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عنوان ژورنال:
  • J. Sci. Comput.

دوره 59  شماره 

صفحات  -

تاریخ انتشار 2014