Complexity of the parallel Givens factorization on shared memory architectures

  • Michel Cosnard
  • Mostafa El Daoudi
  • Yves Robert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 401)


We study the complexity of the parallel Givens factorization of a square matrix of size n on shared memory multicomputers with p processors. We show how to construct an optimal algorithm using a greedy technique. We deduce that the time complexity is equal to:
$$T_{opt} (p) = \frac{{n^2 }}{{2p}} + p + o(n) for 1 \leqslant p \leqslant \frac{n}{{2 + \sqrt 2 }}$$
and that the minimum number of processors in order to compute the Givens factorization in optimal time Topt is equal to Popt=n/2+√2.

These results complete previous analysis presented in the case where the number of processors is unlimited.


Parallel linear algebra complexity of parallel algorithms orthogonal factorization Givens rotations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Michel Cosnard
    • 1
  • Mostafa El Daoudi
    • 1
  • Yves Robert
    • 1
  1. 1.LIP-IMAG Ecole Normale Supérieure de LyonLyon Cedex 07France

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