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Direct Linear Solvers for Vector and Parallel Computers

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Vector and Parallel Processing – VECPAR’98 (VECPAR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1573))

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Abstract

We consider direct methods for the numerical solution of linear systems with unsymmetric sparse matrices. Different strategies for the determination of the pivots are studied. For solving several linear systems with the same pattern structure we generate a pseudo code, that can be interpreted repeatedly to compute the solutions of these systems. The pseudo code can be advantageously adapted to vector and parallel computers. For that we have to find out the instructions of the pseudo code which are independent of each other. Based on this information, one can determine vector instructions for the pseudo code operations (vectorisation) or spread the operations among different processors (parallelisation). The methods are successfully used on vector and parallel computers for the circuit simulation of VLSI circuits as well as for the dynamic process simulation of complex chemical production plants.

This work was supported by the Federal Ministry of Education, Science, Research and Technology, Bonn, Germany under grants GA7FVB-3.0M370 and GR7FV1.

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Author information

Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany

    Friedrich Grund

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  1. Friedrich Grund
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Editors and Affiliations

  1. EUIT Telecomunicación - DIATEL, Universidad Politécnica de Madrid, Ctra., Valencia, Km. 7, 28031, Madrid, Spain

    Vicente Hernández

  2. Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal

    José M. L. M. Palma

  3. Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack J. Dongarra

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© 1999 Springer-Verlag Berlin Heidelberg

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Grund, F. (1999). Direct Linear Solvers for Vector and Parallel Computers. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_10

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  • DOI: https://doi.org/10.1007/10703040_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66228-0

  • Online ISBN: 978-3-540-48516-2

  • eBook Packages: Springer Book Archive

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