Exponential Sum Approximations for tβ

  • William McLeanEmail author


Given β > 0 and δ > 0, the function tβ may be approximated for t in a compact interval [δ, T] by a sum of terms of the form weat, with parameters w > 0 and a > 0. One such an approximation, studied by Beylkin and Monzón (Appl. Comput. Harmon. Anal. 28:131–149, 2010), is obtained by applying the trapezoidal rule to an integral representation of tβ, after which Prony’s method is applied to reduce the number of terms in the sum with essentially no loss of accuracy. We review this method, and then describe a similar approach based on an alternative integral representation. The main difference is that the new approach achieves much better results before the application of Prony’s method; after applying Prony’s method the performance of both is much the same.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia

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