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Parallel Computation of Pseudospectra Using Transfer Functions on a MATLAB-MPI Cluster Platform

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Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2474))

Abstract

One of the most computationally expensive problems in numerical linear algebra is the computation of the ε-pseudospectrum of matrices, that is, the locus of eigenvalues of all matrices of the form A + E, where ‖_E ‖ ≤ є. Several research efforts have been attempting to make the problem tractable by means of better algorithms and utilization of all possible computational resources. One common goal is to bring to users the power to extract pseudospectrum information from their applications, on the computational environments they generally use, at a cost that is sufficiently low to render these computations routine. To this end, we investigate a scheme based on i) iterative methods for computing pseudospectra via approximations of the resolvent norm, with ii) a computational platform based on a cluster of PCs and iii) a programming environment based on MATLAB enhanced with MPI functionality and show that it can achieve high performance for problems of significant size.

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Author information

Authors and Affiliations

  1. Computer Engineering & Informatics Department, University of Patras, Greece

    Constantine Bekas, Efrosini Kokiopoulou & Efstratios Gallopoulos

  2. Mathematics Department, University of Bologna, Italy

    Valeria Simoncini

Authors
  1. Constantine Bekas
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  2. Efrosini Kokiopoulou
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  3. Efstratios Gallopoulos
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  4. Valeria Simoncini
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Editor information

Editors and Affiliations

  1. Abteilung für Graphische und Parallele Datenverarbeitung (GUP) Institut für Technische Informatik und Telematik, Johannes Kepler Universität Linz, Altenbergstr. 69, 4040, Linz, Austria

    Dieter Kranzlmüller  & Jens Volkert  & 

  2. Computer and Automation Research Institute, MTA SZTAKI, Hungarian Academy of Sciences, Victor Hugo u. 18-22, 1132, Budapest, Hungary

    Peter Kacsuk

  3. Computer Science Department Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

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© 2002 Springer-Verlag Berlin Heidelberg

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Bekas, C., Kokiopoulou, E., Gallopoulos, E., Simoncini, V. (2002). Parallel Computation of Pseudospectra Using Transfer Functions on a MATLAB-MPI Cluster Platform. In: Kranzlmüller, D., Volkert, J., Kacsuk, P., Dongarra, J. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2002. Lecture Notes in Computer Science, vol 2474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45825-5_35

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  • DOI: https://doi.org/10.1007/3-540-45825-5_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44296-7

  • Online ISBN: 978-3-540-45825-8

  • eBook Packages: Springer Book Archive

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