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PARASPAR: Parallel solvers for sparse linear algebraic systems

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Parallel Scientific Computing (PARA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 879))

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Abstract

PARASPAR is a package for the solution of linear algebraic systems whose coefficient matrices are large and sparse. Linear least squares problems can also be treated by PARASPAR (using the method of augmentation). Both direct methods and preconditioned iterative procedures are used. The direct methods are based on the classical Gaussian elimination with three different pivotal strategies. The iterative methods used are a modified ORTHOMIN algorithm, CGS, BI-CGSTAB and TFQMR. The preconditioners for all iterative algorithms are calculated by using an approximate LU factorization, which is obtained by dropping small non-zero elements during the Gaussian elimination. If the preconditioners are not sufficiently accurate (and, therefore, the iterative process is either divergent or the convergence is very slow), then an attempt to increase the accuracy of the preconditioner can automatically be performed.

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Author information

Authors and Affiliations

  1. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, DK-4000, Roskilde, Denmark

    Zahari Zlatev

  2. The Danish Computer Centre for Research and Education, UNI-C, DTH, Bldg. 305, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

Authors
  1. Zahari Zlatev
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  2. Jerzy Waśniewski
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Jack Dongarra Jerzy Waśniewski

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© 1994 Springer-Verlag Berlin Heidelberg

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Zlatev, Z., Waśniewski, J. (1994). PARASPAR: Parallel solvers for sparse linear algebraic systems. In: Dongarra, J., Waśniewski, J. (eds) Parallel Scientific Computing. PARA 1994. Lecture Notes in Computer Science, vol 879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030181

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  • DOI: https://doi.org/10.1007/BFb0030181

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58712-5

  • Online ISBN: 978-3-540-49050-0

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