Numerische Mathematik

, Volume 122, Issue 3, pp 527–555

Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix

  • Carla Ferreira
  • Beresford Parlett
  • Froilán M. Dopico

DOI: 10.1007/s00211-012-0470-z

Cite this article as:
Ferreira, C., Parlett, B. & Dopico, F.M. Numer. Math. (2012) 122: 527. doi:10.1007/s00211-012-0470-z


Several relative eigenvalue condition numbers that exploit tridiagonal form are derived. Some of them use triangular factorizations instead of the matrix entries and so they shed light on when eigenvalues are less sensitive to perturbations of factored forms than to perturbations of the matrix entries. A novel empirical condition number is used to show when perturbations are so large that the eigenvalue response is not linear. Some interesting examples are examined in detail.

Mathematics Subject Classification


Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Carla Ferreira
    • 1
  • Beresford Parlett
    • 2
  • Froilán M. Dopico
    • 3
  1. 1.Centro de MatemáticaUniversidade do MinhoBragaPortugal
  2. 2.Division of the EECS Department, Department of Mathematics and Computer ScienceUniversity of CaliforniaBerkeleyUSA
  3. 3.Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM and Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain