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  • Artikel: DFG Deutsche Nationallizenzen  (2)
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  • 1
    Digitale Medien
    Digitale Medien
    The solution of large-scale least-squares problems on supercomputers (1990)
    Springer
    Annals of operations research 22 (1990), S. 241-252 
    Details
    ISSN: 1572-9338
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract We discuss methods for solving medium to large-scale sparse least-squares problems on supercomputers, illustrating our remarks by experiments on the CRAY-2 supercomputer at Harwell. The method we are primarily concerned with is an augmented system approach which has the merit of both robustness and accuracy, in addition to a kernel operation that is just the solution of a symmetric indefinite system. We consider extensions to handle weighted and constrained problems, and include experiments on systems similar to those arising in the Karmarkar algorithm for linear programming. We indicate how recent improvements to the kernel software could greatly improve the performance of the least-squares code.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02023055
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    The effect of ordering on preconditioned conjugate gradients (1989)
    Springer
    BIT 29 (1989), S. 635-657 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 65F10 ; Sparse matrices ; preconditioning ; ordering strategies ; conjugate gradients
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We investigate the effect of the ordering of the unknowns on the convergence of the preconditioned conjugate gradient method. We examine a wide range of ordering methods including nested dissection, minimum degree, and red-black and consider preconditionings without fill-in. We show empirically that there can be a significant difference in the number of iterations required by the conjugate gradient method and suggest reasons for this marked difference in performance. We also consider the effect of orderings when an incomplete factorization which allows some fill-in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through drop tolerances and level of fill-in.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01932738
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Artikel (Nationallizenzen)
    Volltext
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