On the Gibbs Phenomenon 1: Recovering Exponential Accuracy from the Fourier Partial Sum of a Non-Periodic Analytic Function
Abstract
It is well known that the Fourier series of an analytic and periodic function, truncated after 2N+l terms, converges exponentially with N, even in the maximum norm. It is also known that if the function is not periodic, the rate of convergence deteriorates; in particular there is no convergence in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. In this paper we show that the first 2N+l Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed. Gibbs phenomenon, Fourier Series, Exponential accuracy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1992
- Accession Number
- ADA248145
Entities
People
- Alex Solomonoff
- Chi-Wang Shu
- David Gottlieb
- Herve Vandeven