Inexact generalized Noda iterations for generalized eigenproblems

Abstract In this paper, we present an inexact generalized Noda iteration (IGNI) for finding the Perron pair of the generalized eigenproblem arising from economic models. We prove that the approximate eigenvalue sequence generated by IGNI converges globally linearly; Furthermore, we also propose an enhanced inexact generalized Noda iteration(EIGNI), and prove that the approximate eigenvector sequence generated by EIGNI algorithms converges superlinearly. Numerical examples illustrate that the proposed IGNI and EIGNI algorithms are efficient.