Approximating functions on ${\mathbb R}^+$ by exponential sums
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909008813621248 |
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| author | Kuznetsov, Alexey Mohammadioroojeh, Armin |
| author_facet | Kuznetsov, Alexey Mohammadioroojeh, Armin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating functions on ${\mathbb R}^+$ by exponential sums Kuznetsov, Alexey Mohammadioroojeh, Armin Numerical Analysis 41A30, 65D15, 41A21 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. |
| title | Approximating functions on ${\mathbb R}^+$ by exponential sums |
| topic | Numerical Analysis 41A30, 65D15, 41A21 |
| url | https://arxiv.org/abs/2508.19095 |