An analysis of the perturbation error bounds for singular and eigenvalues of diagonally dominant matrices. Issue 1 (1st June 2022)

• Record Type: Journal Article
• Authors: Li, Jiangjiang; Liu, Tianhua
• Is Part Of: Journal of physics. Volume 2282:Issue 1(2022)
• Publication Date: 2022-06-01
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/2282/1/012002
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: 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.