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Hierarchical approach for deriving a reproducible unblocked LU factorization
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).ORCID iD: 0000-0003-2414-700X
Sorbonne Univ, Paris, France..
Univ Perpignan, Perpignan, France..
Univ Jaime I, Castellon de La Plana, Spain..
2019 (English)In: The international journal of high performance computing applications, ISSN 1094-3420, E-ISSN 1741-2846, Vol. 33, no 5, p. 791-803Article in journal (Refereed) Published
Abstract [en]

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). 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.

Place, publisher, year, edition, pages
SAGE PUBLICATIONS LTD , 2019. Vol. 33, no 5, p. 791-803
Keywords [en]
LU factorization, BLAS, reproducibility, accuracy, long accumulator, error-free transformation, GPUs
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-261320DOI: 10.1177/1094342019832968ISI: 000484527300005Scopus ID: 2-s2.0-85072080167OAI: oai:DiVA.org:kth-261320DiVA, id: diva2:1358302
Note

QC 20191007

Available from: 2019-10-07 Created: 2019-10-07 Last updated: 2019-10-07Bibliographically approved

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Iakymchuk, Roman

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  • apa
  • harvard1
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  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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