Optimal filter and mollifier for piecewise smooth spectral data

Optimal filter and mollifier for piecewise smooth spectral data

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the function is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs’ oscillations in the neighborhood of edges and an overall deterioration of the convergence rate to the unacceptable first order. C...

Adaptive Filters for Piecewise Smooth Spectral Data

We introduce a new class of exponentially accurate filters for processing piecewise smooth spectral data. Our study is based on careful error decompositions, focusing on a rather precise balance between physical space localization and the usual moments condition. Exponential convergence is recovered by optimizing the order of the filter as an adaptive function of both the projection order, and ...

Piecewise Smooth Data from its Spectral Information

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs oscillations in the neighborhood of edges and an overall deterioration to the unacceptable rst-order convergence rate. The purpose is ...

Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data

Abstract. This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurat...

Spectral Reconstruction of Piecewise Smooth Functions