Ammar Khellaf - Preparatory Class Department,National Polytechnic College of Constantine (Engineering College), Algeria
Hamza Guebbai - Department of Mathematics, Faculty of Mathematics and Computer Science and Material Sciences, University ۸ May ۱۹۴۵ of Guelma, Algeria
Wassim Merchela - Derzhavin Tambov State University, ۳۳ internatsionalnaya St., Tambov ۳۹۲۰۰۰, Russia
Mohamed Aissaoui - Department of Mathematics, Faculty of Mathematics and Computer Science and Material Sciences, University ۸ May ۱۹۴۵ of Guelma, Algeria

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.

Generalized spectrum approximation, Operator pencil, iterative scheme