Abstract
In this manuscript, we present optimal sensitivity results of eigenvalues and eigenspaces with respect toself-adjoint compact operators. We show that while eigenvalues depend in a Lipschitzian way in compact operators, theeigenspaces are only locally Lipschitz. Our results generalize to arbitrary dimension eigenspaces the results obtained in [19]for one-dimensional eigenspaces sensitivity and thus simplify the celebrate results by Davis and Kahan [6] developedfor general Hermitian operator perturbations. Moreover, Proper Orthogonal Decomposition bases sensitivityis carried out in the case of time-interval perturbations, spatial perturbations (Gappy-POD) or parameter perturbations.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
