On the Gibbs Phenomenon and Its Resolution

摘要: The nonuniform convergence of the Fourier series for discontinuous functions, and in particular oscillatory behavior finite sum, was already analyzed by Wilbraham 1848. This later named Gibbs phenomenon. This article is a review phenomenon from different perspective. phenomenon, as we view it, deals with issue recovering point values function its expansion coefficients. Alternatively it can be viewed possibility recovery local information global information. main theme here not structure oscillations but understanding resolution general setting. The purpose this to show that knowledge coefficients sufficient obtaining piecewise smooth function, same order accuracy case. done using construct different, rapidly convergent, approximation.