, Volume 23, Issue 3, pp 228-242

Asymptotic behavior of Eckhoff’s method for Fourier series convergence acceleration

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Abstract

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called “jumps” is studied and asymptotic L 2 constants of the rate of convergence of the method are computed.