Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized.
@article{M2AN_2001__35_6_1185_0,
author = {Baca\"er, Nicolas},
title = {Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {35},
year = {2001},
pages = {1185-1195},
mrnumber = {1873522},
zbl = {1037.65054},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2001__35_6_1185_0}
}
Bacaër, Nicolas. Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 1185-1195. http://gdmltest.u-ga.fr/item/M2AN_2001__35_6_1185_0/
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