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

{"title":"近线性时间中的功率序列构成","authors":"Yasunori Kinoshita, Baitian Li","doi":"arxiv-2404.05177","DOIUrl":null,"url":null,"abstract":"We present an algebraic algorithm that computes the composition of two power\nseries in $\\mathop{\\tilde{\\mathrm O}}(n)$ time complexity. The previous best\nalgorithms are $\\mathop{\\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS\n2008) and an $\\mathop{\\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger,\nSalvy, Schost and Villard (JACM 2023). Our algorithm builds upon the recent Graeffe iteration approach to manipulate\nrational power series introduced by Bostan and Mori (SOSA 2021).","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"117 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Power Series Composition in Near-Linear Time\",\"authors\":\"Yasunori Kinoshita, Baitian Li\",\"doi\":\"arxiv-2404.05177\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an algebraic algorithm that computes the composition of two power\\nseries in $\\\\mathop{\\\\tilde{\\\\mathrm O}}(n)$ time complexity. The previous best\\nalgorithms are $\\\\mathop{\\\\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS\\n2008) and an $\\\\mathop{\\\\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger,\\nSalvy, Schost and Villard (JACM 2023). Our algorithm builds upon the recent Graeffe iteration approach to manipulate\\nrational power series introduced by Bostan and Mori (SOSA 2021).\",\"PeriodicalId\":501033,\"journal\":{\"name\":\"arXiv - CS - Symbolic Computation\",\"volume\":\"117 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2404.05177\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.05177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - CS - Symbolic Computation

自引率

0.00%

发文量