Approximating the Kohlrausch function by sums of exponentials

Min Zhong, Richard Loy, Robert Anderssen


The Kohlrausch functions \(\exp(−t\beta)\), with \(\beta\in (0, 1)\), which are important in a wide range of physical, chemical and biological applications, correspond to specific realizations of completely monotone functions. In this paper, using nonuniform grids and midpoint estimates, constructive procedures are formulated and analysed for the Kohlrausch functions. Sharper estimates are discussed to improve the approximation results. Numerical results and representative approximations are presented to illustrate the effectiveness of the proposed method.



Kohlrausch function, sums of exponentials, approximation


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.