Perturbed Generalised Taylor's Formulae with Sharp Bounds and Estimation of Relative Entropy
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Cerone, Pietro (2002) Perturbed Generalised Taylor's Formulae with Sharp Bounds and Estimation of Relative Entropy. RGMIA research report collection, 5 (2).
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 mututal information.
| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/17712 |
| Subjects | Historical > FOR Classification > 0102 Applied Mathematics Historical > 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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