{"title":"齐次超立方体上的最优矩阵算法","authors":"G. Fox, W. Furmanski, D. Walker","doi":"10.1145/63047.63125","DOIUrl":null,"url":null,"abstract":"This paper describes a set of concurrent algorithms for matrix algebra, based on a library of collective communication routines for the hypercube. We show how a systematic application of scattering reduces load imbalance. A number of examples are considered (Gaussian elimination, Gauss-Jordan matrix inversion, the power method for eigenvectors, and tridiagonalisation by Householder's method), and the concurrent efficiencies are discussed.","PeriodicalId":299435,"journal":{"name":"Conference on Hypercube Concurrent Computers and Applications","volume":"96 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"Optimal matrix algorithms on homogeneous hypercubes\",\"authors\":\"G. Fox, W. Furmanski, D. Walker\",\"doi\":\"10.1145/63047.63125\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper describes a set of concurrent algorithms for matrix algebra, based on a library of collective communication routines for the hypercube. We show how a systematic application of scattering reduces load imbalance. A number of examples are considered (Gaussian elimination, Gauss-Jordan matrix inversion, the power method for eigenvectors, and tridiagonalisation by Householder's method), and the concurrent efficiencies are discussed.\",\"PeriodicalId\":299435,\"journal\":{\"name\":\"Conference on Hypercube Concurrent Computers and Applications\",\"volume\":\"96 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Conference on Hypercube Concurrent Computers and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/63047.63125\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Conference on Hypercube Concurrent Computers and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/63047.63125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal matrix algorithms on homogeneous hypercubes
This paper describes a set of concurrent algorithms for matrix algebra, based on a library of collective communication routines for the hypercube. We show how a systematic application of scattering reduces load imbalance. A number of examples are considered (Gaussian elimination, Gauss-Jordan matrix inversion, the power method for eigenvectors, and tridiagonalisation by Householder's method), and the concurrent efficiencies are discussed.
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