Computable eigenvalue bounds for rank-k perturbations
Copyright policy )Computable eigenvalue bounds for rank-k perturbations
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 \textit{I. C. F. Ipsen} and \textit{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.
- University of Amsterdam Netherlands
- UNIVERSITEIT VAN AMSTERDAM Netherlands
Bordered diagonal, Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Algebra and Number Theory, singular values, Eigenvalues, Inequalities involving eigenvalues and eigenvectors, 510, low rank Hermitian perturbations, eigenvalue bounds, arrowhead matrix, Arrowhead matrix, Hermitian matrices, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, Geometry and Topology, bordered diagonal
Bordered diagonal, Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Algebra and Number Theory, singular values, Eigenvalues, Inequalities involving eigenvalues and eigenvectors, 510, low rank Hermitian perturbations, eigenvalue bounds, arrowhead matrix, Arrowhead matrix, Hermitian matrices, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, Geometry and Topology, bordered diagonal
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