A distributed packed storage for large dense parallel in-core calculations

In this paper we propose a distributed packed storage format that exploits the symmetry or the triangular structure of a dense matrix. This format stores only half of the matrix while maintaining most of the efficiency compared with a full storage for a wide range of operations. This work has been m...

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Bibliographic Details
Published in:Concurrency and computation Vol. 19; no. 4; pp. 483 - 502
Main Authors: Baboulin, Marc, Giraud, Luc, Gratton, Serge, Langou, Julien
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 25.03.2007
Wiley
Subjects:
Cholesky factorization
dense linear algebra
Mathematics
packed storage format
parallel distributed algorithms
QR factorization
ScaLAPACK
scientific computing
ISSN:1532-0626, 1532-0634
Online Access:Get full text
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Summary:In this paper we propose a distributed packed storage format that exploits the symmetry or the triangular structure of a dense matrix. This format stores only half of the matrix while maintaining most of the efficiency compared with a full storage for a wide range of operations. This work has been motivated by the fact that, in contrast to sequential linear algebra libraries (e.g. LAPACK), there is no routine or format that handles packed matrices in the currently available parallel distributed libraries. The proposed algorithms exclusively use the existing ScaLAPACK computational kernels, which proves the generality of the approach, provides easy portability of the code and provides efficient re‐use of existing software. The performance results obtained for the Cholesky factorization show that our packed format performs as good as or better than the ScaLAPACK full storage algorithm for a small number of processors. For a larger number of processors, the ScaLAPACK full storage routine performs slightly better until each processor runs out of memory. Copyright © 2006 John Wiley & Sons, Ltd.
Bibliography:istex:35756EDEBFF07B63523910749ADFEE30C818C964
ArticleID:CPE1119
ark:/67375/WNG-B6N6PJC4-G
ISSN:1532-0626
1532-0634
DOI:10.1002/cpe.1119