1. bookVolume 7 (2021): Issue 1 (January 2021)
Journal Details
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First Published
16 Apr 2015
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2 times per year
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English
access type Open Access

Sigmoid functions for the smooth approximation to the absolute value function

Published Online: 22 Nov 2020
Page range: 12 - 19
Received: 26 Jul 2020
Accepted: 17 Oct 2020
Journal Details
License
Format
Journal
First Published
16 Apr 2015
Publication timeframe
2 times per year
Languages
English

We present smooth approximations to the absolute value function |x| using sigmoid functions. In particular, x erf(x/μ) is proved to be a better smooth approximation for |x| than x tanh(x/μ) and x2+μ\sqrt {{x^2} + \mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.

Keywords

MSC 2010

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