Pipeline Givens sequences for computing the QR decomposition on a EREW PRAM

Authors:
Marc Hofmann;Erricos John Kontoghiorghes
Affiliations:
Institut d'informatique, Université de Neuchítel, Emile-Argand 11, Case Postale 2, CH-2007 Neuchítel, Switzerland;Department of Public and Business Administration, University of Cyprus, Cyprus and School of Computer Science and Information Systems, Birkbeck College, University of London, UK
Venue:
Parallel Computing
Year:
2006

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Abstract

Parallel Givens sequences for computing the QR decomposition of an mxn (mn) matrix are considered. The Givens rotations operate on adjacent planes. A pipeline strategy for updating the pair of elements in the affected rows of the matrix is employed. This allows a Givens rotation to use rows that have been partially updated by previous rotations. Two new Givens schemes, based on this pipeline approach, and requiring respectively n^2/2 and n processors, are developed. Within this context a performance analysis on an exclusive-read, exclusive-write (EREW) parallel random access machine (PRAM) computational model establishes that the proposed schemes are twice as efficient as existing Givens sequences.