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  • Engineering  (2)
  • 2005-2009
  • 1995-1999  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Multifrontal QR Factorization in a Multiprocessor Environment (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 275-300 
    Details
    ISSN: 1070-5325
    Keywords: sparse QR factorization ; multifrontal method ; parallelism ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Performance issues for frontal schemes on a cache-based high-performance computer (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 127-143 
    Details
    ISSN: 0029-5981
    Keywords: unsymmetric sparse matrices ; frontal solver ; direct methods ; finite elements ; BLAS ; computational kernels ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high-performance computer where data must be in the cache before arithmetic operations can be performed on it. In particular, we show how we can modify the frontal solution algorithm to enhance the proportion of arithmetic operations performed using Level 3 BLAS thus enabling better reuse of data in the cache. We illustrate the effects of this on Silicon Graphics Power Challenge machines using problems which arise in real engineering and industrial applications. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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