If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, “On the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra,” in Theory and Practice of Control and Systems (Proceedings of the 6th IEEE Mediterranean Conference on Control and Systems, Alghero, Italy, June 1998) (A. Tornambè, G. Conte, and A.M. Perdon, eds.)...

The main objective and contribution of this paper consists in using a formal and mathematical approach to prove that parallel computer processing systems are better than serial computer processing systems, better related to: saving time and/or money and being able to solve larger problems. This is achieved thanks to the theory of Lyapunov stability and max-plus algebra applied to discrete event...

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce a...

Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...

We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings semifields idempotent addition. Given a set samples, each consisting input output an unknown function defined on semifield, problem is to find function, by Puiseux polynomial rational functions. A solution approach proposed, involves reduction approximate...

This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analogues of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we ...