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European Symposium on Algorithms

ESA 1996: Algorithms — ESA '96 pp 290–301Cite as

Parallel complexity of householder QR factorization

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1136))

Abstract

Gaussian Elimination with Partial Pivoting and Householder QR factorization are two very popular methods to solve linear systems. Implementations of these two methods are provided in state-of-the-art numerical libraries and packages, such as LAPACK and MATLAB. Gaussian Elimination with Partial Pivoting was already known to be P-complete. Here we prove that the Householder QR factorization is likely to be inherently sequential as well. We also investigate the problem of speedup vs non degeneracy and accuracy in numerical algorithms.

Partially supported by the ESPRIT III Basic Research Programme of the EC under contract No. 9072 (Project GEPPCOM) and by MURST 40% and 60% funds.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125, Pisa, Italy

    Mauro Leoncini

  2. Dipartimento di Scienze e Tecnologie Avanzate, Università di Torino, Via Cavour 84, 15100, Alessandria, Italy

    Giovanni Manzini

  3. Istituto di Matematica Computazionale, Via S. Maria, 46, 56126, Pisa, Italy

    Giovanni Manzini

  4. Dipartimento Scienze dell'Informazione, Università di Bologna, Piazza Porta S. Donato 5, 40127, Bologna, Italy

    Luciano Margara

Authors
  1. Mauro Leoncini
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  2. Giovanni Manzini
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  3. Luciano Margara
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Editor information

Josep Diaz Maria Serna

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© 1996 Springer-Verlag Berlin Heidelberg

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Leoncini, M., Manzini, G., Margara, L. (1996). Parallel complexity of householder QR factorization. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_63

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  • DOI: https://doi.org/10.1007/3-540-61680-2_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61680-1

  • Online ISBN: 978-3-540-70667-0

  • eBook Packages: Springer Book Archive

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