The Galerkin method for perturbed self-adjoint operators and applications
Michael Strauss · Journal of Spectral Theory · 2014
We consider the Galerkin method for approximating the spectrum of an operator T+A where T is semi-bounded self-adjoint and A satisfies a relative compactness condition. We show that the method is reliable in all regions where it is reliable for the unperturbed problem - which always contains \mathbb{C}\backslash\mathbb{R} . The results lead to a new technique for identifying eigenvalues of T , and for identifying spectral pollution which arises from applying the Galerkin method directly to T . The new technique benefits from being applicable on the form domain.