Tropical diagonal scaling for asymptotic eigenvalue problems

Andrea Marchesini (1, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 MAXPLUS - Max-plus algebras and mathematics of decision

We study the behaviour of the eigenvalues of a parametric matrix polynomial P in a neighbourhood of zero. If we suppose that the entries of P have Puiseux series expansion, we can build an auxiliary matrix polynomial Q whose entries are the leading exponents of those of P. We show that preconditioning P via a diagonal scaling based on the tropical eigenvalues of Q can improve conditioning and backward error of the eigenvalues.

Domaines: Théorie spectrale [math.SP]

Andrea Marchesini. Tropical diagonal scaling for asymptotic eigenvalue problems. The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Aug 2015, Beijing, China. ⟨hal-01253175⟩