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Title: Parallel strategies for rank-k updating of the qr decomposition
Authors: Kontoghiorghes, Erricos John 
Keywords: Parallel algorithms
Issue Date: 2000
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM Journal on Matrix Analysis and Applications, 2000, Volume 22, Issue 3, Pages 714-725
Abstract: arallel strategies based on Givens rotations are proposed for updating the QR decomposition of an n × n matrix after a rank-k change (k < n). The complexity analyses of the Givens algorithms are based on the total number of Givens rotations applied to a 2-element vector. The algorithms, which are extensions of the rank-1 updating method, achieve the updating using approximately 2(k + n) compound disjoint Givens rotations (CDGRs) with elements annihilated by rotations in adjacent planes. Block generalization of the serial rank-1 algorithms are also presented. The algorithms are rich in level 3 BLAS operations, making them suitable for implementation on large scale parallel systems. The performance of some of the algorithms on a 2-D SIMD (single instruction stream-multiple instruction stream) array processor is discussed.
ISSN: 0895-4798 (print)
1095-7162 (online)
DOI: 10.1137/S0895479896308585
Rights: © 2000 Society for Industrial and Applied Mathematics.
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