Foundations of Computational Mathematics

, Volume 3, Issue 2, pp 207–223

Perturbation of Eigenpairs of Factored Symmetric Tridiagonal Matrices

  •  Parlett

DOI: 10.1007/s10208-001-0051-5

Cite this article as:
Parlett Found. Comput. Math. (2003) 3: 207. doi:10.1007/s10208-001-0051-5


Suppose that an indefinite symmetric tridiagonal matrix permits triangular factorization T = LDLt . We provide individual condition numbers for the eigenvalues and eigenvectors of T when the parameters in L and D suffer small relative perturbations. When there is element growth in the factorization, then some pairs may be robust while others are sensitive. A 4 × 4 example shows the limitations of standard multiplicative perturbation theory and the efficacy of our new condition numbers.

Key words. Eigenvalues, Perturbation, Tridiagonal. AMS Classification. Primary, 6540; Secondary, 1525.

Copyright information

© 2002 Society for the Foundation of Computational Mathema tics

Authors and Affiliations

  •  Parlett
    • 1
  1. 1.Mathematics Department and Computer Science Division of the EECS Department University of California Berkeley, CA 94720, USA parlett@math.berkeley.eduUS