Tiskin, Alexander (2002) Bulk-synchronous parallel Gaussian elimination. Journal of Mathematical Sciences, Volume 108 (Number 6). pp. 977-991. doi:10.1023/A:1013588221172

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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
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	Journal of Mathematical Sciences
Publisher:	Springer Verlag
ISSN:	1072-3374
Official Date:	1 March 2002
Dates:	Date Event 1 March 2002 Published
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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