Article

Numerische Mathematik

, Volume 122, Issue 3, pp 527-555

First online:

Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix

  • Carla FerreiraAffiliated withCentro de Matemática, Universidade do Minho Email author 
  • , Beresford ParlettAffiliated withDivision of the EECS Department, Department of Mathematics and Computer Science, University of California
  • , Froilán M. DopicoAffiliated withInstituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM and Departamento de Matemáticas, Universidad Carlos III de Madrid

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Abstract

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

65F15