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

作　　者：Jicheng Li Jing Wu Xu Kong 

机构地区：[1]School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

出　　处：《Journal of Applied Mathematics and Physics》2014年第3期60-70,共11页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Singular Value Eigenvalue Perturbation HERMITIAN MATRIX BLOCK TRIDIAGONAL MATRIX EIGENVECTOR 

分 类 号：O1[理学—数学]