Parallel Computations of Spectral Portraits of Matrices and Applications to System Stability Analysis


Keywords: parallel processing, matrices, stability analysis, singular value decomposition

Start Date: 1 February 95 / Status: finished / Duration: 18 months

[ participants / contact]

Objectivies and Approach

This project aims to design and implement several parallel algorithms for plotting the spectral portrait of a matrix and to study the application of this technique to the stability analysis of several types of system. Necessary research is carried out to provide good solutions to the computation of spectral portraits of matrices, and develop prototype codes.

The research part concentrates on the following major tasks :

The development part will provide a set of prototype codes dedicated to regular arrays of processors for computing the spectral portraits of dense matrices from regular grids.

Progress and Results

The computation consists of the calculation of the smallest singular value of a matrix with a complex parameter that takes its values on a rectangular grid. At the conclusion of the project, two parallel Jacobi algorithms and an algorithm based on the bidiagonalisation of matrices -for dense matrices- as well as a parallel Davidson method -for sparse matrices- were designed and tested on an Intel-Paragon computer with 56 processors. The largest orders of the matrices tested were 1000 for dense matrices and 8000 for sparse matrices on 50x50 grids.

Information Dissemination Activities and/or Exploitation

This project will be followed by the project STABLE which aims at the use of the results obtained in applications, in particular in computational fluid dynamics.


Campus de Beaulieu
F-35042 Rennes Cedex, F

EU Partners


Non-EU Partners

Institute for Informatics Slovak Academy of Sciences, SK
Institute of Mathematics of the Siberian Branch of the
Russian Academy of Sciences, RU
Centre for Informatics and Computer Technology, Sofia, BG


Prof. Bernard Philippe
Tel: +33 99 84 73 38
Fax: +33 99 84 71 71

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PORTRAIT - CP94-682, May 1997

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html version of synopsis by Nick Cook