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Efficient Algorithms for the Block Hessenberg Form

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Abstract

We investigate in this paper the performance of parallel algorithms for computing the controllable part of a control linear system, with application to the computation of minimal realizations. Our approach is based on a method that transforms the matrices of the system to block Hessenberg form by using rank-revealing orthogonal factorizations.

The experimental analysis on a high performance architecture includes two rank-revealing numerical tools: the SVD and the rank-revealing QR factorizations. Results are also reported, using the rank-revealing QR factorizations, on a parallel distributed architecture.

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Authors and Affiliations

  1. Dept. de Informática, Univ. Jaime I, 12080, Castellón, Spain

    Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí & Maribel Castillo

  2. Dept. de Sistemas Informáticos y Computación, Univ. Politécnica de Valencia, 46071, Valencia, Spain

    Vicente Hernández

Authors
  1. Enrique S. Quintana-Ortí
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  2. Gregorio Quintana-Ortí
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  3. Maribel Castillo
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  4. Vicente Hernández
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Quintana-Ortí, E.S., Quintana-Ortí, G., Castillo, M. et al. Efficient Algorithms for the Block Hessenberg Form. The Journal of Supercomputing 20, 55–66 (2001). https://doi.org/10.1023/A:1011192320367

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