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Estimation of Relative Entropy Using Novel Taylor-Like Representations

Cerone, Pietro (2002) Estimation of Relative Entropy Using Novel Taylor-Like Representations. RGMIA research report collection, 5 (4).

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Abstract

Sharp bounds are obtained for perturbed generalised Taylor series. The perturbation involves the arithmetic sum of the upper and lower bounds of the (n+1)th derivative. The sharpest bound is in terms of the one norm of the Appell polynomial which constitutes the coefficients of the derivative of the function to be approximated. The results are demonstrated for the estimation of the Kullback-Leibler distance, Shannon entropy and mutual information.

Item Type: Article
Uncontrolled Keywords: perturbed generalised Taylor’s formula, Appell polynomials, Sharp bounds, Čebyšev-type functional, Kullback-Leibler distance, entropy, mutual information
Subjects: FOR Classification > 0102 Applied Mathematics
FOR Classification > 0103 Numerical and Computational Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 30 Aug 2012 01:36
Last Modified: 24 May 2013 04:12
URI: http://vuir.vu.edu.au/id/eprint/17790
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