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For this purpose, we build upon Level-1\/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated in a high performance and stable algorithm for the (blocked) LU factorization.<\/jats:p>","DOI":"10.1177\/1094342019832968","type":"journal-article","created":{"date-parts":[[2019,3,17]],"date-time":"2019-03-17T23:14:25Z","timestamp":1552864465000},"page":"791-803","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Hierarchical approach for deriving a reproducible unblocked LU factorization"],"prefix":"10.1177","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2414-700X","authenticated-orcid":false,"given":"Roman","family":"Iakymchuk","sequence":"first","affiliation":[{"name":"KTH Royal Institute of Technology, Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stef","family":"Graillat","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Defour","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Perpignan, Perpignan, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrique S","family":"Quintana-Ort\u00ed","sequence":"additional","affiliation":[{"name":"Universidad Jaime I, Castell\u00f3n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,3,17]]},"reference":[{"key":"bibr1-1094342019832968","volume-title":"Efficient reproducible floating point summation and BLAS","author":"Ahrens P","year":"2016"},{"key":"bibr2-1094342019832968","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPS.2014.127"},{"key":"bibr3-1094342019832968","unstructured":"Bainville E (2010) OpenCL\n                      GEMV\n                      . 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