Estimation of Relative Entropy Using Novel Taylor-Like Representations

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


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
Subjects Current > FOR Classification > 0102 Applied Mathematics
Current > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords perturbed generalised Taylor’s formula, Appell polynomials, Sharp bounds, Čebyšev-type functional, Kullback-Leibler distance, entropy, mutual information
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