NEW BOUNDS FOR SHANNON, RELATIVE AND MANDELBROT ENTROPIES VIA ABEL-GONTSCHAROFF INTERPOLATING POLYNOMIAL
NEW BOUNDS FOR SHANNON, RELATIVE AND MANDELBROT ENTROPIES VIA ABEL-GONTSCHAROFF INTERPOLATING POLYNOMIAL
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DOI：
10.7153/mia-2019-22-88
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发表时间：
2019-10-01
影响因子：
1
通讯作者：
Pecaric, Josip
中科院分区：
文献类型：
--
作者：
Butt, Saad Ihsan;Mehmood, Nasir;Pecaric, Josip
詹森不等式在现代分析的许多领域都有很大的影响。它有助于计算信息论中使用的几个熵度量的有用上界。利用新的格林函数和Abel-Gontschamff插值多项式，将Jensen不等式的离散和连续循环精化从凸函数推广到高阶凸函数.作为我们工作的一个应用，我们建立了Shanon熵、相对熵和Mandelbrot熵的新的熵界之间的联系。
The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We use discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions and Abel-Gontschamff interpolating polynomial. As an application of our work, we establish connection among new entropic bounds for Shanon, Relative and Mandelbrot entropies.