Journal of Applied Mathematics and Physics

Volume 2, Issue 3 (February 2014)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.70  Citations  

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

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DOI: 10.4236/jamp.2014.23007    3,352 Downloads   5,245 Views  
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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.

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Li, J. , Wu, J. and Kong, X. (2014) Application and Generalization of Eigenvalues Perturbation Bounds for Hermitian Block Tridiagonal Matrices. Journal of Applied Mathematics and Physics, 2, 60-70. doi: 10.4236/jamp.2014.23007.

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