Computable eigenvalue bounds for rank-\(k\) perturbations. (English) Zbl 1195.15019
The authors investigate lower bounds for the eigenvalues of low rank Hermitian perturbations of Hermitian matrices and for the singular values of low rank perturbations of general matrices. They show that, for the smallest eigenvalue, some earlier results of Weyl and of I. C. F. Ipsen and B. Nadler [SIAM J. Matrix Anal. Appl. 31, 40–53 (2009; Zbl 1189.15022)] are the first two of a sequence of increasingly tight bounds. Generally the \(q\)th element of the sequence is an eigenvalue of a \(q\times q\) matrix.
Reviewer: Alan L. Andrew (Bundoora)
MSC:
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
Keywords:
eigenvalue bounds; arrowhead matrix; bordered diagonal; low rank Hermitian perturbations; Hermitian matrices; singular valuesCitations:
Zbl 1189.15022Software:
IPSENReferences:
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