An analysis of the perturbation error bounds for singular and eigenvalues of diagonally dominant matrices

In this paper, we investigate the error bounds of singular values and eigenvalues for diagonally dominant Hermite matrices when the matrix on its off-diagonal entries and on diagonally dominant part is perturbed with bound ε . Our results show that not only is the bound independent of the condition...

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Bibliographic Details
Published in:Journal of physics. Conference series 2022-06, Vol.2282 (1), p.12002
Main Authors: Li, Jiangjiang, Liu, Tianhua
Format: Article
Language:English
Subjects:
Eigenvalues
Error analysis
Mathematical analysis
Perturbation
Physics
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Summary:In this paper, we investigate the error bounds of singular values and eigenvalues for diagonally dominant Hermite matrices when the matrix on its off-diagonal entries and on diagonally dominant part is perturbed with bound ε . Our results show that not only is the bound independent of the condition number of the matrix, but the matrix itself need not be symmetric positive definite. Furthermore, the bounds are applicable to both the eigenvalue and singular value of the matrix and can be used in generalized eigenvalue problems.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2282/1/012002