ENO-Wavelet Transforms for Piecewise Smooth Functions

ENO-Wavelet Transforms for Piecewise Smooth Functions

We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across ju...

9 . Adaptive ENO - Wavelet Transforms for Discontinuous Functions

We have desiged an adaptive ENO-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the one-side information idea from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing to standard wavelet transforms. This transform retains the essential properties and advantages of standard wavelet transforms ...

Adaptive Eno - Wavelet Transforms for Discontinuousfunctions

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored t...

Approximating Piecewise-Smooth Functions

We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...