适用于所有有限群的快速广义 DFT

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2024-09-04 DOI:10.1137/20m1316342

Chris Umans

{"title":"适用于所有有限群的快速广义 DFT","authors":"Chris Umans","doi":"10.1137/20m1316342","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Computing, Ahead of Print. <br/> Abstract. For any finite group [math], we give an algebraic algorithm to compute the generalized discrete Fourier transform with respect to [math], using [math] operations, for any [math]. Here, [math] is the exponent of matrix multiplication.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast Generalized DFTs for All Finite Groups\",\"authors\":\"Chris Umans\",\"doi\":\"10.1137/20m1316342\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Computing, Ahead of Print. <br/> Abstract. For any finite group [math], we give an algebraic algorithm to compute the generalized discrete Fourier transform with respect to [math], using [math] operations, for any [math]. Here, [math] is the exponent of matrix multiplication.\",\"PeriodicalId\":49532,\"journal\":{\"name\":\"SIAM Journal on Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1137/20m1316342\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1137/20m1316342","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 计算期刊》，提前印刷。摘要。对于任意有限群 [math]，我们给出了一种代数算法，对于任意 [math]，使用 [math] 运算计算关于 [math] 的广义离散傅里叶变换。这里，[math] 是矩阵乘法的指数。

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

Fast Generalized DFTs for All Finite Groups

SIAM Journal on Computing, Ahead of Print.
Abstract. For any finite group [math], we give an algebraic algorithm to compute the generalized discrete Fourier transform with respect to [math], using [math] operations, for any [math]. Here, [math] is the exponent of matrix multiplication.

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

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.