Smoothing Approximations for Some Piecewise Smooth

Authors: Hao Wu Peng Zhang GuiHua Lin

Publish Date: 2015/07/17

Volume: 3, Issue: 3, Pages: 317-329

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Abstract

In this paper we study smoothing approximations for some piecewise smooth functions We first present two approaches for onedimensional case a global approach is to construct smoothing approximations over the whole domain and a local approach is to construct smoothing approximations within appropriate neighborhoods of the nonsmooth points We obtain some error estimate results for both approaches and discuss whether the smoothing approximations can inherit the convexity of the original functions Furthermore we extend the global approach to some multiple dimensional cases

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