Convergence of Approximation Methods to Compute Eigenelements of Linear Operations

The object of this paper is a theoretical study of the convergence of approximation methods (Galerkin and finite difference methods) to compute eigenelements of a closed linear operator T in a Banach space. The stability and strong stability of the approximation method are defined, and they reduce to very simple conditions when T is self-adjoint, either compact, or bounded from below with compact resolvent.