, Volume 3, Issue 2, pp 207-223

Perturbation of Eigenpairs of Factored Symmetric Tridiagonal Matrices

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Abstract.

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.