Approximating the kohlrausch function by sums of exponentials

Min Zhong; R. J. Loy; R. S. Anderssen

doi:10.1017/S1446181113000229

Approximating the kohlrausch function by sums of exponentials

Min Zhong^*, R. J. Loy, R. S. Anderssen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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. ©

Original language	English
Pages (from-to)	306-323
Number of pages	18
Journal	ANZIAM Journal
Volume	54
Issue number	4
DOIs	https://doi.org/10.1017/S1446181113000229
Publication status	Published - Apr 2013

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abstract = "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. {\textcopyright}",

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T1 - Approximating the kohlrausch function by sums of exponentials

AU - Zhong, Min

AU - Loy, R. J.

AU - Anderssen, R. S.

PY - 2013/4

Y1 - 2013/4

N2 - 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. ©

AB - 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. ©

KW - Kohlrausch function

KW - approximation

KW - sums of exponentials

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U2 - 10.1017/S1446181113000229

DO - 10.1017/S1446181113000229

M3 - Article

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VL - 54

SP - 306

EP - 323

JO - ANZIAM Journal

JF - ANZIAM Journal

IS - 4

ER -

Approximating the kohlrausch function by sums of exponentials

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