Mathieu Faverge, J. Langou, Y. Robert, J. Dongarra
{"title":"Bidiagonalization and R-Bidiagonalization: Parallel Tiled Algorithms, Critical Paths and Distributed-Memory Implementation","authors":"Mathieu Faverge, J. Langou, Y. Robert, J. Dongarra","doi":"10.1109/IPDPS.2017.46","DOIUrl":null,"url":null,"abstract":"We study tiled algorithms for going from a \"full\" matrix to a condensed \"band bidiagonal\" form using orthog-onal transformations: (i) the tiled bidiagonalization algorithm BIDIAG, which is a tiled version of the standard scalar bidiago-nalization algorithm; and (ii) the R-bidiagonalization algorithm R-BIDIAG, which is a tiled version of the algorithm which consists in first performing the QR factorization of the initial matrix, then performing the band-bidiagonalization of the R- factor. For both BIDIAG and R-BIDIAG, we use four main types of reduction trees, namely FLATTS, FLATTT, GREEDY, and a newly introduced auto-adaptive tree, AUTO. We provide a study of critical path lengths for these tiled algorithms, which shows that (i) R-BIDIAG has a shorter critical path length than BIDIAG for tall and skinny matrices, and (ii) GREEDY based schemes are much better than earlier proposed algorithms with unbounded resources. We provide experiments on a single multicore node, and on a few multicore nodes of a parallel distributed shared- memory system, to show the superiority of the new algorithms on a variety of matrix sizes, matrix shapes and core counts.","PeriodicalId":209524,"journal":{"name":"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IPDPS.2017.46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We study tiled algorithms for going from a "full" matrix to a condensed "band bidiagonal" form using orthog-onal transformations: (i) the tiled bidiagonalization algorithm BIDIAG, which is a tiled version of the standard scalar bidiago-nalization algorithm; and (ii) the R-bidiagonalization algorithm R-BIDIAG, which is a tiled version of the algorithm which consists in first performing the QR factorization of the initial matrix, then performing the band-bidiagonalization of the R- factor. For both BIDIAG and R-BIDIAG, we use four main types of reduction trees, namely FLATTS, FLATTT, GREEDY, and a newly introduced auto-adaptive tree, AUTO. We provide a study of critical path lengths for these tiled algorithms, which shows that (i) R-BIDIAG has a shorter critical path length than BIDIAG for tall and skinny matrices, and (ii) GREEDY based schemes are much better than earlier proposed algorithms with unbounded resources. We provide experiments on a single multicore node, and on a few multicore nodes of a parallel distributed shared- memory system, to show the superiority of the new algorithms on a variety of matrix sizes, matrix shapes and core counts.