近线性时间中的功率序列构成

arXiv - CS - Symbolic Computation Pub Date : 2024-04-08 DOI:arxiv-2404.05177

Yasunori Kinoshita, Baitian Li

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引用次数: 0

摘要

我们提出了一种代数算法，可以在 $\mathop\{tilde{\mathrm O}}(n)$ 时间复杂度内计算两个幂级数的组成。之前的最佳算法是 Kedlaya 和 Umans 的 $\mathop{\mathrm O}(n^{1+o(1)})$ 算法（FOCS2008），以及 Neiger,Salvy,Schost 和 Villard 的 $\mathop{\mathrm O}(n^{1.43})$ 代数算法（JACM 2023）。我们的算法建立在 Bostan 和 Mori (SOSA 2021) 最近提出的操纵幂级数的 Graeffe 迭代方法之上。

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Power Series Composition in Near-Linear Time

We present an algebraic algorithm that computes the composition of two power series in $\mathop{\tilde{\mathrm O}}(n)$ 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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arXiv - CS - Symbolic Computation

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