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Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix |
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| Authors: | Carla Ferreira Beresford Parlett Froilán M. Dopico |
| Affiliation: | 1. Centro de Matem??tica, Universidade do Minho, 4710-057, Braga, Portugal 2. Division of the EECS Department, Department of Mathematics and Computer Science, University of California, Berkeley, CA, 94720, USA 3. Instituto de Ciencias Matem??ticas CSIC-UAM-UC3M-UCM and Departamento de Matem??ticas, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911, Legan??s, Spain |
| 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. |
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