𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the power method in max algebra

✍ Scribed by Ludwig Elsner; P.van den Driessche

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
140 KB
Volume
302-303
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

The eigenvalue problem for an irreducible nonnegative matrix e ij in the max algebra system is e x kx, where e x i max j ij x j and k turns out to be the maximum circuit geometric mean, le. A power method algorithm is given to compute le and eigenvector x. The algorithm is developed by using results on the convergence of max powers of e, which are proved using nonnegative matrix theory. In contrast to an algorithm developed in , this new method works for any irreducible nonnegative e, and calculates eigenvectors in a simpler and more ecient way. Some asymptotic formulas relating le, the spectral radius and norms are also given.

πŸ“œ SIMILAR VOLUMES

On matrix powers in max-algebra
On matrix powers in max-algebra
✍ P. Butkovič; R.A. Cuninghame-Green πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 165 KB
A note on the characteristic equation in
A note on the characteristic equation in the max-plus algebra
✍ Bart De Schutter; Bart De Moor πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 635 KB

We discuss the characteristic equation of a matrix in the max-plus algebra. In their Linear Algebra Appl. paper [101:87-108 (1988)] Olsder and Roos have used a transformation between the max-plus algebra and linear algebra to show that the Cayley-Hamilton theorem also holds in the maw-plus algebra.

On the boolean minimal realization probl
On the boolean minimal realization problem in the max-plus algebra
✍ Bart De Schutter; Vincent Blondel; Remco de Vries; Bart De Moor πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 127 KB

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results in connection with the minimal realization problem in the max-plus algebra. First we characterize the minimal system order of a max-li