Multifrontal QR factorization in a multiprocessor environment (1994)
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BibTeX
@MISC{Amestoy94multifrontalqr,
author = {P. Amestoy and I.S. Duff and C. Puglisi},
title = {Multifrontal QR factorization in a multiprocessor environment},
year = {1994}
}
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Abstract
We describe the design and implementation of a parallel QR decomposition algorithm for a large sparse matrix A. The algorithm is based on the multifrontal approach and makes use of Householder transformations. The tasks are distributed among processors according to an assembly tree which is built from the symbolic factorization of the matrix A T A. Uniprocessor issues are first addressed. We then discuss the multiprocessor implementation of the method. Parallelization of both the factorization phase and the solve phase are considered. We use relaxation of the sparsity structure of both the original matrix and the frontal matrices to improve the performance. We show that, in this case, the use of Level 3 BLAS can lead to very significant performance improvement. The eight processor Alliant FX/80 is used to illustrate our discussion. 1 ENSEEIHT-IRIT (Toulouse, France), amestoy@enseeiht.fr. 2 CERFACS (Toulouse, France) also Rutherford App leton Lab., (England), duff@cerfac...
