J. Barlow and I. Slapnicar, “Optimal Perturbation Bounds for the Hermitian Eigenvalue Problem,” Linear Algebra and its Applications, Vol. 309, No. 1-3, 2000, pp. 19-43.

has been cited by the following article:

• TITLE: Application and Generalization of Eigenvalues Perturbation Bounds for Hermitian Block Tridiagonal Matrices

  AUTHORS: Jicheng Li, Jing Wu, Xu Kong

  KEYWORDS: Singular Value; Eigenvalue Perturbation; Hermitian Matrix; Block Tridiagonal Matrix; Eigenvector

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.3, February 25, 2014

  ABSTRACT: 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.