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In this paper, we introduce a Prony-type data fitting problem consisting in interpolating the table \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ m, g(m)\right\} _{m=0}^M$$\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g(0)\ne 0$$\end{document} in the sense of least squares by exponential sums with equal weights. We further study how to choose the parameters of the sums properly to solve the problem. Moreover, we show that the sums have some advantages in data fitting over the classical Prony exponential sums. Namely, we prove that the parameters of our sums are a priori well-controlled and thus can be found via a stable numerical framework, in contrast to those of the Prony ones. In several numerical experiments, we also compare the behaviour of both the sums and illustrate the above-mentioned advantages.

Data Fitting by Exponential Sums with Equal Weights