A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra

In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is proposed. Given a matrix of finite size, the problem consists in giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrent equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrent equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed.