Generalized iterative scheme for a generalized spectral problem

In this work, we define an iterative scheme for a generalized spectral problem associated with two operators defined on a Banach space of infinite dimension. We show that under the norm convergence, the generalized approximated eigenvalues and eigenvectors converge to the exact eigenpairs. As a numerical application, we tackle a generalized eigenvalue problem associated with integral operators, where the accuracy and efficiency are illustrated in some numerical examples.

Keywords:

Generalized spectrum approximation , Operator pencil , iterative scheme