Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications

Mathematics

Nikolay Kyurkchiev¹ 

[1] Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria;

关键词: exponentially optimal adaptive filter;    Hausdorff distance;    upper and lower bounds;    activation function;    modified families of functions with “polynomial variable transfer”;   

DOI  :  10.3390/math8111963

来源: DOAJ

【 摘 要 】

In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type $F\left(t\right)$ by the class of exponential functions ${\sigma }_{adapt}\left(t\right)$ about the Hausdorff metric. We prove upper and lower estimates for “saturation”—d (in the case $q=2$). New activation and “semi-activation” functions based on ${\sigma }_{adapt}\left(t\right)$ are defined. Some related problems are discussed. We also consider modified families of functions with “polynomial variable transfer”. Numerical examples, illustrating our results using CAS MATHEMATICA are given.

【 授权许可】

Unknown