|Title:|| REMARKS ON THE FOURIER-
|Authors:|| L. Vozovoi, M. Israeli and A. Averbuch
|Abstract:||In this paper we investigate some numerical aspects of the Fourier-Gegenbauer method introduced in . The asymptotic behavior of the Gegenbauer series is analyzed as well as the behavior of this series with small and moderate numbers of terms. A new criteria for obtaining an exponentially small truncation error is found. It is shown that the exponential convergence takes place only for the short-term Gegenbauer expansion. The computed Fourier-Gegenbauer expansion with a large number of terms exhibits the Gibbs phenomenon in spite of the fact that both the resolution and the truncation errors are exponentially small.|
|Copyright||The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information|
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