Perturbation of Eigenpairs of Factored Symmetric Tridiagonal Matrices
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Suppose that an indefinite symmetric tridiagonal matrix permits triangular factorization T = LDL t . 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.
- Perturbation of Eigenpairs of Factored Symmetric Tridiagonal Matrices
Foundations of Computational Mathematics
Volume 3, Issue 2 , pp 207-223
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- Key words. Eigenvalues, Perturbation, Tridiagonal. AMS Classification. Primary, 6540; Secondary, 1525.
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- A1. Mathematics Department and Computer Science Division of the EECS Department University of California Berkeley, CA 94720, USA firstname.lastname@example.org, US