Numerical Algorithms

, Volume 46, Issue 4, pp 351–368

Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function

  • Sergio Barrachina
  • Peter Benner
  • Enrique S. Quintana-Ortí
Original Paper

DOI: 10.1007/s11075-007-9143-x

Cite this article as:
Barrachina, S., Benner, P. & Quintana-Ortí, E.S. Numer Algor (2007) 46: 351. doi:10.1007/s11075-007-9143-x


We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory. Here, we discuss algorithms based on a generalization of the Newton iteration for the matrix sign function. The algorithms are easy to parallelize and provide an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.


Bernoulli equation Linear and nonlinear matrix equations Matrix sign function Control and systems theory Parallel linear algebra libraries 

Mathematics Subject Classifications (2000)

65F30 93C05 93D15 65Y05 

Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  • Sergio Barrachina
    • 1
  • Peter Benner
    • 2
  • Enrique S. Quintana-Ortí
    • 1
  1. 1.Depto. de Ingeniería y Ciencia de ComputadoresUniversidad Jaume ICastellón de la PlanaSpain
  2. 2.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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