Refined perturbation bounds for eigenvalues of Hermitian and non-Hermitian matrices. (English) Zbl 1189.15022
The authors present refined perturbation bounds for the eigenvalues of a Hermitian matrix subjected to different kinds of Hermitian as well as non-Hermitian perturbations. The change in eigenvalues is expressed in terms of a projection of the perturbation onto a particular eigenspace, rather than in terms of the full perturbation. Applications to principal component analysis under a spiked covariance model, and pseudo arclength continuation methods for the solution of nonlinear systems are considered.
Reviewer: C. M. da Fonseca (Coimbra)
MSC:
15A42 | Inequalities involving eigenvalues and eigenvectors |
65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
65H10 | Numerical computation of solutions to systems of equations |
65H17 | Numerical solution of nonlinear eigenvalue and eigenvector problems |
65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
15A18 | Eigenvalues, singular values, and eigenvectors |
15B57 | Hermitian, skew-Hermitian, and related matrices |