Variational Properties and Rayleigh Quotient Algorithms for Symmetric Matrix Pencils

  • Peter Lancaster
  • Qiang Ye
Part of the Operator Theory: Advances and Applications book series (OT, volume 40)


We consider matrix pencils λA — B in which λ is a complex parameter, A, B are both hermitian and A is nonsingular. Variational characterizations of the real eigenvalues (if any) are formulated. Rayleigh quotient algorithms for finding real eigenvalues are proposed and their local and global convergence properties are established and illustrated.


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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Peter Lancaster
    • 1
  • Qiang Ye
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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