The paper
contains two parts. First, by applying the results about the eigenvalue perturbation
bounds for Hermitian block tridiagonal matrices in paper [1], we obtain a new
efficient method to estimate the perturbation bounds for singular values of
block tridiagonal matrix. Second, we consider the perturbation bounds for eigenvalues
of Hermitian matrix with block tridiagonal structure when its two adjacent
blocks are perturbed simultaneously. In this case, when the eigenvalues of the
perturbed matrix are well-separated from the spectrum of the diagonal blocks,
our eigenvalues perturbation bounds are very sharp. The numerical examples
illustrate the efficiency of our methods.
References
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