{"title":"Caltech Mark II超立方体上具有旋转的高斯-乔丹反演","authors":"P. Hipes, A. Kuppermann","doi":"10.1145/63047.63123","DOIUrl":null,"url":null,"abstract":"The performance of a parallel Gauss-Jordan matrix inversion<supscrpt>1,2</supscrpt> algorithm on the Mark II hypercube<supscrpt>3</supscrpt> at Caltech is discussed. We will show that parallel Gauss-Jordan inversion is superior to parallel Gaussian elimination <italic>for inversion</italic>, and discuss the reasons for this. Empirical and theoretical efficiencies for parallel Gauss-Jordan inversion as a function of matrix dimension for different numbers and configurations of processors are presented. The theoretical efficiencies are in <italic>quantitative</italic> agreement with the empirical efficiencies.","PeriodicalId":299435,"journal":{"name":"Conference on Hypercube Concurrent Computers and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Gauss-Jordan inversion with pivoting on the Caltech Mark II hypercube\",\"authors\":\"P. Hipes, A. Kuppermann\",\"doi\":\"10.1145/63047.63123\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The performance of a parallel Gauss-Jordan matrix inversion<supscrpt>1,2</supscrpt> algorithm on the Mark II hypercube<supscrpt>3</supscrpt> at Caltech is discussed. We will show that parallel Gauss-Jordan inversion is superior to parallel Gaussian elimination <italic>for inversion</italic>, and discuss the reasons for this. Empirical and theoretical efficiencies for parallel Gauss-Jordan inversion as a function of matrix dimension for different numbers and configurations of processors are presented. The theoretical efficiencies are in <italic>quantitative</italic> agreement with the empirical efficiencies.\",\"PeriodicalId\":299435,\"journal\":{\"name\":\"Conference on Hypercube Concurrent Computers and Applications\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Conference on Hypercube Concurrent Computers and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/63047.63123\",\"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/10.1145/63047.63123","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gauss-Jordan inversion with pivoting on the Caltech Mark II hypercube
The performance of a parallel Gauss-Jordan matrix inversion1,2 algorithm on the Mark II hypercube3 at Caltech is discussed. We will show that parallel Gauss-Jordan inversion is superior to parallel Gaussian elimination for inversion, and discuss the reasons for this. Empirical and theoretical efficiencies for parallel Gauss-Jordan inversion as a function of matrix dimension for different numbers and configurations of processors are presented. The theoretical efficiencies are in quantitative agreement with the empirical efficiencies.
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