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Title: Parallel algorithms for downdating the least squares estimator of the regression model
Authors: Yanev, Petko I. 
Kontoghiorghes, Erricos John 
Keywords: Least squares;Parallel algorithms;Communication systems;Problem solving;Regression analysis
Category: Economics and Business
Field: Social Sciences
Issue Date: 2008
Publisher: Elsevier
Source: Parallel Computing, 2008, Volume 34, Issue 6-8, Pages 451-468
Journal: Parallel Computing 
Abstract: Computationally efficient parallel algorithms for downdating the least squares estimator of the ordinary linear regression are proposed. The algorithms, which are based on the QR decomposition, are block versions of sequential Givens strategies and efficiently exploit the triangular structure of the data matrices. The first strategy utilizes only part of the orthogonal matrix which is derived from the QR decomposition of the initial data matrix. The rest of the orthogonal matrix is not updated or explicitly computed. A modification of the parallel algorithm, which explicitly computes the whole orthogonal matrix in the downdated QR decomposition, is also considered. An efficient distribution of the matrices over the processors is proposed. Furthermore, the new algorithms do not require any inter-processor communication. The theoretical complexities are derived and experimental results are presented and analyzed. The parallel strategies are scalable and highly efficient for large scale downdating least squares problems. A new parallel block-hyperbolic downdating strategy is developed. The algorithm is rich in BLAS-3 computations, involves negligible duplicated computations and requires insignificant inter-processor communication. It is found to outperform the previous downdating strategies and to be highly efficient for large scale problems. The experimental results confirm the derived theoretical complexities.
ISSN: 01678191
Rights: © 2008 Elsevier B.V. All rights reserved.
Type: Article
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