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@incollection{faucris.269967580,
abstract = {This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how these can be approximated using Γ-convergence. We review several flows from literature, which were proposed to compute nonlinear eigenfunctions, and show that they all relate to normalized gradient flows. Furthermore, we show that the implicit Euler discretization of gradient flows gives rise to a nonlinear power method of the proximal operator and we demonstrate their convergence to nonlinear eigenfunctions. Finally, we prove that Γ-convergence of functionals implies convergence of their ground states.},
author = {Bungert, Leon and Burger, Martin},
doi = {10.1016/bs.hna.2021.12.013},
editor = {Emmanuel Trélat, Enrique Zuazua, Enrique Zuazua, Enrique Zuazua},
faupublication = {yes},
keywords = {Gamma-convergence; Gradient flows; Ground states; Nonlinear eigenvalue problems; Nonlinear power methods},
month = {Jan},
note = {CRIS-Team Scopus Importer:2022-02-25},
pages = {427-465},
peerreviewed = {unknown},
publisher = {Elsevier B.V.},
series = {Handbook of Numerical Analysis},
title = {{Gradient} flows and nonlinear power methods for the computation of nonlinear eigenfunctions},
volume = {23},
year = {2022}
}