33 citations · 72 across the 5 of their papers we have counts for
5 papers
Iteration of order preserving subhomogeneous maps on a cone
Marianne Akian, Stephane Gaubert, Bas Lemmens +1
We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit co…
Discrete max-plus spectral theory
Marianne Akian, Stephane Gaubert, Cormac Walsh
We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning…
Set coverings and invertibility of Functional Galois Connections
Marianne Akian, Stephane Gaubert, Vassili Kolokoltsov
We consider equations of the form Bf=g, where B is a Galois connection between lattices of functions. This includes the case where B is the Legendre-Fenchel transform, or more gene…
Perturbation of eigenvalues of matrix pencils and optimal assignment problem
Marianne Akian, Ravindra Bapat, Stephane Gaubert
We consider a matrix pencil whose coefficients depend on a positive parameter , and have asymptotic equivalents of the form when goes to zero, where the leading coeff…
Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem
Marianne Akian, Ravindra Bapat, Stephane Gaubert
We extend the perturbation theory of Vishik, Ljusternik and Lidskii for eigenvalues of matrices, using methods of min-plus algebra. We show that the asymptotics of the eigenvalues…