Generalized iterative scheme for a generalized spectral problem

Khellaf, Ammar; Guebbai, Hamza; Merchela, Wassim; Aissaoui, Mohamed Zine

doi:10.22075/ijnaa.2022.24614.2782

Generalized iterative scheme for a generalized spectral problem

Document Type : Research Paper

Authors

Ammar Khellaf ¹

Hamza Guebbai ²

Wassim Merchela ³

Mohamed Zine Aissaoui ²

¹ Preparatory Class Department,National Polytechnic College of Constantine (Engineering College), Algeria

² Department of Mathematics, Faculty of Mathematics and Computer Science and Material Sciences, University 8 May 1945 of Guelma, Algeria

³ Derzhavin Tambov State University, 33 internatsionalnaya St., Tambov 392000, Russia

10.22075/ijnaa.2022.24614.2782

Abstract

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