Approximating functions on ${\mathbb R}^+$ by exponential sums

Alexey Kuznetsov; Armin Mohammadioroojeh

doi:10.1016/j.cam.2026.117756

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arXiv · 2508.19095

Approximating functions on ${\mathbb R}^+$ by exponential sums

Alexey Kuznetsov·Armin Mohammadioroojeh

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Abstract

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace transform and employs a highly efficient continued fraction technique to construct the corresponding rational approximant. We demonstrate the accuracy of this method through a variety of examples, including the Gaussian function, probability density functions of the lognormal and Gompertz-Makeham distributions, the hockey stick and unit step functions, as well as a function arising in the approximation of the gamma and Barnes $G$-functions.

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Alexey Kuznetsov, Armin Mohammadioroojeh. 2025-08-26. Approximating functions on ${\mathbb R}^+$ by exponential sums. https://doi.org/10.1016/j.cam.2026.117756

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