On the Gibbs phenomenon V:
recovering exponential accuracy from
collocation point values of a piecewise analytic
function |
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Authors: | David Gottlieb Chi-Wang Shu |
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Institution: | (1) Division of Applied Mathematics, Brown University, Providence, RI 02912, USA , US |
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Abstract: | Summary.
This paper presents a method to recover
exponential accuracy at all points (including at the
discontinuities themselves), from the knowledge
of an approximation to the
interpolation polynomial (or trigonometrical polynomial).
We show that if we are given the collocation point values
(or a highly accurate approximation) at the Gauss
or Gauss-Lobatto points,
we can reconstruct an uniform exponentially convergent
approximation to the function in any sub-interval
of analyticity. The proof covers the cases of Fourier,
Chebyshev, Legendre, and more
general Gegenbauer collocation methods.
A numerical example is also provided.
Received
July 17, 1994 / Revised version received December 12, 1994 |
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Keywords: | Mathematics Subject Classification (1991): 42A15 41A05 41A25 |
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