Approximating functions on \mathbb R⁺ by exponential sums

2025/08/26 by Kuznetsov, Alexey, Mohammadioroojeh, Armin
#41A21 #41A30 #65D15 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.19095

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 Padé 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.

Citations

• Differential approximation of the Gaussian by short cosine sums with exponential error decay
• On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents
• Computing the Barnes G-function and the gamma function in the entire complex plane
• From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
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