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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 79 (1991), S. 169-174 
    ISSN: 1432-2234
    Schlagwort(e): Gaussian elimination ; Sparse linear equations ; Multifrontal method ; Vectorization ; Parallelization ; Elimination tree
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary In the last decade, the development in computer architectures has strongly influenced and motivated the evolution of algorithms for large-scale scientific computing. The unifying theme of the parallel algorithm group in CERFACS is the exploitation of vector and parallel computers in the solution of large-scale problems arising in computational science and engineering. The choice of a portable approach often leads to a loss in the average performance per computer with respect to a machine dependent implementation of the code. However, we show that, in full linear algebra as well as in sparse linear algebra, efficiency and portability can be combined. To illustrate our approach, we discuss results obtained on a wide range of shared memory multiprocessors including the Alliant FX/80, the IBM 3090E/3VF, the IBM 3090J/6VF, the CRAY-2, and the CRAY Y-MP.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 275-300 
    ISSN: 1070-5325
    Schlagwort(e): sparse QR factorization ; multifrontal method ; parallelism ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: 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 ATA.We first address uniprocessor issues and then discuss the multiprocessor implementation of the method. We consider the parallelization of both the factorization phase and the solve phase. 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 gains in performance. We use the eight processor Alliant˜FX/80 at CERFACS to illustrate our discussion.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Publikationsdatum: 2013-07-01
    Print ISSN: 0004-6361
    Digitale ISSN: 1432-0746
    Thema: Physik
    Publiziert von EDP Sciences
    Standort Signatur Erwartet Verfügbarkeit
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