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

Nikolay Kyurkchiev
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Nikolay Kyurkchiev: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24, Tzar Asen Str., 4000 Plovdiv, Bulgaria

Mathematics, 2020, vol. 8, issue 11, 1-15

Abstract: 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 ( t ) by the class of exponential functions σ a d a p t ( t ) 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 σ a d a p t ( t ) 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.

Keywords: exponentially optimal adaptive filter; Hausdorff distance; upper and lower bounds; activation function; modified families of functions with “polynomial variable transfer” (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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