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Bulk-synchronous parallel Gaussian elimination
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Tiskin, Alexander (2002) Bulk-synchronous parallel Gaussian elimination. Journal of Mathematical Sciences, Volume 108 (Number 6). pp. 977-991. doi:10.1023/A:1013588221172 ISSN 1072-3374.
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Official URL: http://dx.doi.org/10.1023/A:1013588221172
Abstract
The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We study the BSP complexity of Gaussian elimination and related problems. First, we analyze the Gaussian elimination without pivoting, which can be applied to the LU decomposition of symmetric positive-definite or diagonally dominant real matrices. Then we analyze the Gaussian elimination with Schönhage's recursive local pivoting suitable for the LU decomposition of matrices over a finite field, and for the QR decomposition of real matrices by the Givens rotations. Both versions of Gaussian elimination can be performed with an optimal amount of local computation, but optimal communication and synchronization costs cannot be achieved simultaneously. The algorithms presented in the paper allow one to trade off communication and synchronization costs in a certain range, achieving optimal or near-optimal cost values at the extremes
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Journal or Publication Title: | Journal of Mathematical Sciences | ||||
Publisher: | Springer Verlag | ||||
ISSN: | 1072-3374 | ||||
Official Date: | 1 March 2002 | ||||
Dates: |
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Volume: | Volume 108 | ||||
Number: | Number 6 | ||||
Page Range: | pp. 977-991 | ||||
DOI: | 10.1023/A:1013588221172 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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