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Title: QR factorization of a dense matrix on a shared-memory multiprocessor

Abstract

A new algorithm for computing an orthogonal decomposition of a rectangular m x n matrix A on a shared-memory parallel computer is described. The algorithm uses Givens rotations, and has the feature that its synchronization cost is low. In particular, for a multiprocessor having p processors, an analysis of the algorithm shows that this cost is O (n/sup 2//p) if m/p greater than or equal to n, and O (mn/p/sup 2/) if m/p < n. Note that in the latter case, the synchronization cost is smaller than O (n/sup 2//p). Therefore, the synchronization cost of the algorithm proposed in this article is bounded by O (n/sup 2//p) when m greater than or equal to n. This is important for machines where synchronization cost is high, and when m >> n. Analysis and experiments show that the algorithm is effective in balancing the load and producing high efficiency (speed-up). 13 refs.

Authors:
;
Publication Date:
Research Org.:
Oak Ridge National Lab., TN (USA)
OSTI Identifier:
5928811
Report Number(s):
ORNL/TM-10581
ON: DE88001506
DOE Contract Number:  
AC05-84OR21400
Resource Type:
Technical Report
Resource Relation:
Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATRICES; FACTORIZATION; PARALLEL PROCESSING; ALGORITHMS; ARRAY PROCESSORS; COST ESTIMATION; EFFICIENCY; MEMORY MANAGEMENT; PERFORMANCE; MATHEMATICAL LOGIC; PROGRAMMING; 990210* - Supercomputers- (1987-1989)

Citation Formats

Chu, E., and George, A. QR factorization of a dense matrix on a shared-memory multiprocessor. United States: N. p., 1987. Web. doi:10.2172/5928811.
Chu, E., & George, A. QR factorization of a dense matrix on a shared-memory multiprocessor. United States. https://doi.org/10.2172/5928811
Chu, E., and George, A. Thu . "QR factorization of a dense matrix on a shared-memory multiprocessor". United States. https://doi.org/10.2172/5928811. https://www.osti.gov/servlets/purl/5928811.
@article{osti_5928811,
title = {QR factorization of a dense matrix on a shared-memory multiprocessor},
author = {Chu, E. and George, A.},
abstractNote = {A new algorithm for computing an orthogonal decomposition of a rectangular m x n matrix A on a shared-memory parallel computer is described. The algorithm uses Givens rotations, and has the feature that its synchronization cost is low. In particular, for a multiprocessor having p processors, an analysis of the algorithm shows that this cost is O (n/sup 2//p) if m/p greater than or equal to n, and O (mn/p/sup 2/) if m/p < n. Note that in the latter case, the synchronization cost is smaller than O (n/sup 2//p). Therefore, the synchronization cost of the algorithm proposed in this article is bounded by O (n/sup 2//p) when m greater than or equal to n. This is important for machines where synchronization cost is high, and when m >> n. Analysis and experiments show that the algorithm is effective in balancing the load and producing high efficiency (speed-up). 13 refs.},
doi = {10.2172/5928811},
url = {https://www.osti.gov/biblio/5928811}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1987},
month = {10}
}