111 citations · 694 across the 56 of their papers we have counts for
7 papers · 1 filter
Non-archimedean valuations of eigenvalues of matrix polynomials
Marianne Akian, Ravindra Bapat, Stéphane Gaubert
We establish general weak majorization inequalities, relating the leading exponents of the eigenvalues of matrices or matrix polynomials over the field of Puiseux series with the t…
Tropical bounds for eigenvalues of matrices
Marianne Akian, Stéphane Gaubert, Andrea Marchesini
We show that for all k = 1,...,n the absolute value of the product of the k largest eigenvalues of an n-by-n matrix A is bounded from above by the product of the k largest tropical…
Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots
Marianne Akian, Stephane Gaubert, Meisam Sharify
We show that the sequence of moduli of the eigenvalues of a matrix polynomial is log-majorized, up to universal constants, by a sequence of "tropical roots" depending only on the n…
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…
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…