{"title":"矩阵乘法加速的域扩展和三线性聚合、统一和消去","authors":"V. Pan","doi":"10.1109/SFCS.1979.17","DOIUrl":null,"url":null,"abstract":"The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schönhage's Theorem about partial and total MM, our approach gives the exponent 2.6054 by the price of a serious increase of the constant.","PeriodicalId":311166,"journal":{"name":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","volume":"161 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1979-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"49","resultStr":"{\"title\":\"Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplications\",\"authors\":\"V. Pan\",\"doi\":\"10.1109/SFCS.1979.17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schönhage's Theorem about partial and total MM, our approach gives the exponent 2.6054 by the price of a serious increase of the constant.\",\"PeriodicalId\":311166,\"journal\":{\"name\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"volume\":\"161 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"49\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1979.17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1979.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 49
摘要
矩阵乘法的加速是基于D. Bini, M. Capovani, G. Lotti, F. Romani和S. Winograd的代数域扩展方法和作者的三线性聚集、统一和抵消方法的结合。推导了一个复杂度为0 (N2.7378)的N × N矩阵乘法快速算法。利用a . Schönhage关于偏MM和总MM的定理,我们的方法给出了指数2.6054,该指数是常数大幅增加的价格。
Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplications
The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schönhage's Theorem about partial and total MM, our approach gives the exponent 2.6054 by the price of a serious increase of the constant.