19 research outputs found
Polynomial eigenvalue solver based on tropically scaled Lagrange linearization
We propose an algorithm to solve polynomial eigenvalue problems via linearization combining several ingredients:
a specific choice of linearization, which is constructed using input from tropical algebra and the notion of
well-separated tropical roots, an appropriate scaling applied to the linearization and a modified stopping criterion for the iterations that takes advantage of the properties of our scaled linearization.
Numerical experiments suggest that our polynomial eigensolver computes all the finite and well-conditioned eigenvalues to high relative accuracy even when they are very different in magnitude.status: publishe