Eigenvalues of rank-one perturbed Hermitian matrices

Jan Brandts
Korteweg-de Vries Institute for Mathematics
University of Amsterdam
Amsterdam, The Netherlands


Abstract:

One of the most basic topics in matrix perturbation theory is the effect of a rank-one update to a matrix on its eigendata. After reviewing some well-know results, we present new bounds on the perturbed eigenvalues due to Ipsen and Nadler (2007).

We show that those new bounds are part of a family of bounds of increasing quality at increasing computational costs, and present some experimental and theoretical results.