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A New Smoothing Approach for Piecewise Smooth Functions: Application to Some Fundamental Functions

Lecture Notes in Networks and Systems, ISSN: 2367-3389, Vol: 476 LNNS, Page: 164-178
2023
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Conference Paper Description

This article is about a new smoothing method for piecewise smooth functions. This smoothing method is based on formulating any piecewise smooth function as the expectation of a discrete random variable. By adopting this formulation, we show that smoothing apiecewise smooth function is equivalent to smooth a probability distribution. In addition, we propose to use the Boltzmann distribution as a smoothing approximation for this probability distribution. We apply our smoothing approach to smooth some fundamental functions. The theoretical and numerical results show the efficiency of our method.

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