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

Abstract

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.Mathematics Subject Classification: 08C99, 16Y60, 65F15, 05C50, 15A29, 15A33

A Note on the Solution of the Characteristic Equation Over the Symmetrized Max-Plus Algebra

“…Based on De Schutter and De Moor's statement, there is the following theorem about necessary and sufficient conditions for the extended complementary linear problem ( [14], [15]). A multivariate polynomial system of equations and inequalities in max-plus algebra if and only if it is an ELCP.…”