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arXiv · 2404.05177

Power Series Composition in Near-Linear Time

Yasunori Kinoshita·Baitian Li
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Abstract

We present an algebraic algorithm that computes the composition of two power series in softly linear time complexity. The previous best algorithms are $\mathop{\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS 2008) and an $\mathop{\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger, Salvy, Schost and Villard (JACM 2023). Our algorithm builds upon the recent Graeffe iteration approach to manipulate rational power series introduced by Bostan and Mori (SOSA 2021).

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BibTeXRIS

Yasunori Kinoshita, Baitian Li. 2024-04-08. Power Series Composition in Near-Linear Time. https://arxiv.org/abs/2404.05177

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