Rayleigh quotient algorithms for nonsymmetric matrix pencils

  • A. AmiraslaniEmail author
  • P. Lancaster
Original Paper


A classical Rayleigh-quotient iterative algorithm (known as “broken iteration”) for finding eigenvalues and eigenvectors is applied to semisimple regular matrix pencils A − λB. It is proved that cubic convergence is attained for eigenvalues and superlinear convergence of order three for eigenvectors. Also, each eigenvalue has a local basin of attraction. A closely related Newton algorithm is examined. Numerical examples are included.


Rayleigh quotient algorithm Matrix pencils 


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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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