2 research outputs found
On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function
It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed
Resolution de quelques problemes en analyse numerique des methodes spectrales
SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc