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Abstract: . We present a parallel algorithm for the QR decomposition with column pivoting of a sparse matrix by means of Modified GramSchmidt orthogonalization. Nonzero elements of the matrix M to decompose are stored in a one-dimensional doubly linked list data structure. A strategy to reduce fill-in is discussed to get memory savings and decrease the computation times. As an application of QR decomposition, we describe the least squares problem. This algorithm has been designed for a message passing... (Update)
Context of citations to this paper: More
.... The design of the corresponding parallel algorithms used for obtaining the experimental results in the next sections are described in [1], 2] and [14] for MGS, Householder and Givens, respectively. We assume a mesh topology and a cyclic distribution of data (double...
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6: The John Hopkins University Press (context) - Golub, Van Loan - 1989
6: User's Guide for the Harwell-Boeing Sparse Matrix Collection (context) - Duff, Grimes et al. - 1982
5: Sparse Householder QR Factorization on a Mesh - Doallo, no et al. - 1996
BibTeX entry: (Update)
R. Doallo, B.B. Fraguela, J. Touri~no and E.L. Zapata (1996), "Parallel Sparse Modified GramSchmidt QR Decomposition", Int'l. Symp. on High-Performance Computing and Networking (HPCN), Brussels, Belgium, pp. 646--653 (Springer-Verlag, LNCS 1067). http://citeseer.ist.psu.edu/article/doallo96parallel.html More
@inproceedings{ doallo96parallel,
author = "Ramon Doallo and Basilio B. Fraguela and Juan Tourino and Emilio L. Zapata",
title = "Parallel Sparse Modified Gram-Schmidt {QR} Decomposition",
booktitle = "{HPCN} Europe",
pages = "646-653",
year = "1996",
url = "citeseer.ist.psu.edu/article/doallo96parallel.html" }
Citations (may not include all citations):2441 The Johns Hopkins University Press (context) - Golub, Van Loan - 1989
322 Direct Methods for Sparse Matrices (context) - Duff, Erisman et al. - 1986
88 User's Guide for the Harwell-Boeing Sparse Matrix Collection (context) - Duff, Grimes et al. - 1992
45 Data Distributions for Sparse Matrix Vector Multiplication - Romero, Zapata - 1995
12 Adaptive Blocking in the QR Factorization (context) - Bischof - 1989
10 Modified Gram-Schmidt QR Factorization on Hypercube SIMD Com.. (context) - Zapata, Lamas et al. - 1991
9 Sparse LU Factorization Cray TD - Sparse, on et al. - 1995
8 Sparsity Analysis of the QR Factorization (context) - Hare, Johnson et al. - 1993
7 Sparse Householder QR Factorization on a Mesh - Doallo, Touri et al. - 1996
6 Sparse QR Factorization on a Massively Parallel Computer (context) - Kratzer - 1992
5 Sparse Givens QR Factorization on a Multiprocessor - no, Doallo et al.
4 Implementation of QR up and Downdating on a Massively Parall.. - Bendtsen, Hansen et al. - 1995
4 Parallel QR Factorization Using the Torus-Wrap Mapping (context) - Hendrickson - 1993
4 Parallel Gram-Schmidt Orthogonalisation on a Network of Tran.. (context) - Waring, Clint - 1991
2 This article was processed using the L a T E X macro package.. (context) - Research, Cray et al. - 1993
The graph only includes citing articles where the year of publication is known.
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Analyzing Data Structures for Parallel Sparse.. - Tourino, Doallo.. (1996) (Correct)
Experimental Evaluation of Efficient Sparse Matrix.. - Ujaldón, Zapata.. (1996) (Correct)
Efficient Parallel Solution of a Semiconductor Laser Array .. - Romero, Zapata, Ramos (1996) (Correct)
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