Parallel complexity of householder QR factorization

  • Mauro Leoncini
  • Giovanni Manzini
  • Luciano Margara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Mauro Leoncini
    • 1
  • Giovanni Manzini
    • 2
    • 3
  • Luciano Margara
    • 4
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly
  2. 2.Dipartimento di Scienze e Tecnologie AvanzateUniversità di TorinoAlessandriaItaly
  3. 3.Istituto di Matematica ComputazionalePisaItaly
  4. 4.Dipartimento Scienze dell'InformazioneUniversità di BolognaBolognaItaly

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