Concentrated real-pole uniform-in-time approximation of the matrix exponential
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917107808075776 |
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| author | Güttel, Stefan Shao, Shuai |
| author_facet | Güttel, Stefan Shao, Shuai |
| contents | We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions $\exp(-tz)$ for $z \geq 0$ and $t$ in a positive time interval $T$. Our result extends a classical result by J.-E.Andersson [J.Approx.Theory, 32(2):85--95, 1981] on the asymptotic best rational approximation of $\exp(-z)$ with real poles. Numerical experiments demonstrate the near-optimality of our choice for various time ranges and for both small and large approximation degrees. An application of the uniform-in-time rational approximation using our proposed concentrated real poles to a linear constant-coefficient initial-value problem is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentrated real-pole uniform-in-time approximation of the matrix exponential Güttel, Stefan Shao, Shuai Numerical Analysis We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions $\exp(-tz)$ for $z \geq 0$ and $t$ in a positive time interval $T$. Our result extends a classical result by J.-E.Andersson [J.Approx.Theory, 32(2):85--95, 1981] on the asymptotic best rational approximation of $\exp(-z)$ with real poles. Numerical experiments demonstrate the near-optimality of our choice for various time ranges and for both small and large approximation degrees. An application of the uniform-in-time rational approximation using our proposed concentrated real poles to a linear constant-coefficient initial-value problem is also discussed. |
| title | Concentrated real-pole uniform-in-time approximation of the matrix exponential |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.21858 |