绝对值函数光滑逼近的Sigmoid函数

Q3 Mathematics

Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI:10.2478/mjpaa-2021-0002

Yogesh J. Bagul, C. Chesneau

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引用次数: 7

摘要

摘要我们使用sigmoid函数给出了绝对值函数|x|的光滑近似。特别地，在精度方面，x erf（x/μ）被证明是|x|比x tanh（x/微米）和x2+μ\sqrt｛{x^2｝+\mu｝更好的光滑近似。为了实现我们的目标，我们还为误差函数提供了尖锐的双曲边界。

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Sigmoid functions for the smooth approximation to the absolute value function

Abstract 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.

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来源期刊

Moroccan Journal of Pure and Applied Analysis Mathematics-Numerical Analysis

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

8 weeks