Asymptotic behavior of Eckhoff’s method for Fourier series convergence acceleration
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- Barkhudaryan, A., Barkhudaryan, R. & Poghosyan, A. Analys in Theo Applic (2007) 23: 228. doi:10.1007/s10496-007-0228-0
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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 L2 constants of the rate of convergence of the method are computed.