On the Convergence of the Goerisch Method for Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum

Abstract

It was shown recently in [13] that the Goerisch method provides upper and lower bounds to eigenvalues of variationally posed self-adjoint eigenvalue problems with arbitrary spectrum. In the present paper the approximation of eigenelements is established. In addition, the convergence of the eigenvalue and eigenelement approximations is shown in a pure func-tional analytic procedure. A numerical example is given where the curve veering phenomenon occurs.