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|Title:||Greedy givens algorithms for computing the rank-k updating of the qr decomposition||Authors:||Kontoghiorghes, Erricos John||Keywords:||Computational complexity;Algorithms||Issue Date:||2002||Publisher:||Elsevier||Source:||Parallel Computing, 2002, Volume 28, Issue 9, Pages 1257-1273||Abstract:||A Greedy Givens algorithm for computing the rank-1 updating of the QR decomposition is proposed. An exclusive-read exclusive-write parallel random access machine computational model is assumed. The complexity of the algorithms is calculated in two different ways. In the unlimited parallelism case a single time unit is required to apply a compound disjoint Givens rotation of any size. In the limited parallelism case all the disjoint Givens rotations can be applied simultaneously, but one time unit is required to apply a rotation to a two-element vector. The proposed Greedy algorithm requires approximately 5/8 the number of steps performed by the conventional sequential Givens rank-1 algorithm under unlimited parallelism. A parallel implementation of the sequential Givens algorithm outperforms the Greedy one under limited parallelism. An adaptation of the Greedy algorithm to compute the rank-k updating of the QR decomposition has been developed. This algorithm outperforms a recently reported parallel method for small k, but its efficiency decreases as k increases||URI:||http://ktisis.cut.ac.cy/handle/10488/6791||ISSN:||01678191||DOI:||http://dx.doi.org/10.1016/S0167-8191(02)00132-1||Rights:||© 2002 Elsevier Science B.V. All rights reserved.||Type:||Article|
|Appears in Collections:||Άρθρα/Articles|
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