Work

Power Series Composition in Near-Linear Time

Year: 2024

Type: conference-paper

Abstract: We present an algebraic algorithm that computes the composition of two power series in softly linear time complexity. The previous best algorithms are$\mathrm{O}(n^{1+o(1)})$non-alzebraic algorithm by Kedlaya and Umans (FOCS 2008) and an$\mathrm{O}(n^{1.43})$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).

Source: Annual Symposium on Foundations of Computer Science

DOI: 10.1109/focs61266.2024.00127

Authors: Yasunori Kinoshita, Baitian Li

Institutions: Tokyo Institute of Technology, Tsinghua University

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Japan Science and Technology Agency

Award: 離散数学、グラフアルゴリズム、グラフ理論の横断的研究