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arXiv · 2606.13965

A remark on Chebyshev rational functions, multipoint Pad\'e approximants and Noise

Maxim Derevyagin·Max Meynig
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Abstract

Motivated by the recent interest in multipoint Pad\'e approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Pad\'e approximants in exactly the same way that Chebyshev polynomials produce Pad\'e approximants. We present recurrence relations for Chebyshev rational functions, as well as the underlying continued fraction of Thiele type (also known as $R_{II}$ type). Finally, we provide numerical evidence illustrating the effects of noise on this interpolation scheme and show that a phenomenon similar to that recently observed by Costin, Dunne, and Meynig for Pad\'e approximants also occurs in the multipoint setting.

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Maxim Derevyagin, Max Meynig. 2026-06-11. A remark on Chebyshev rational functions, multipoint Pad\'e approximants and Noise. https://arxiv.org/abs/2606.13965

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