Hungarian Scaling of Polynomial Eigenproblems

Marianne Akian (1, 2) , Stephane Gaubert (1, 2) , Andrea Marchesini (2, 1) , Françoise Tisseur (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 MAXPLUS - Max-plus algebras and mathematics of decision
3 University of Manchester [Manchester]

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 expansions 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: Analyse numérique [math.NA]; Théorie spectrale [math.SP]

Marianne Akian, Stephane Gaubert, Andrea Marchesini, Françoise Tisseur. Hungarian Scaling of Polynomial Eigenproblems . SIAM Conference on Applied Linear Algebra (SIAM LA), Oct 2015, Atlanta, United States. ⟨hal-01252398⟩