GENERATING SERIES : A COMBINATORIAL COMPUTATION
Résumé
The purpose of this paper is to apply combinatorial techniques for computing coefficients of rational formal series (Gk) in two noncommuting variables and their differences at orders k and k-1. This in turn may help one to study the reliability and the quality of a model for non-linear black-box identification. We investigate the quality of the model throughout the criteria of a measure of convergence. We provide, by a symbolic computation, a valuation relating to the convergence of the family (Bk). This computation is a sum of differ- ential monomials in the input functions and behavior system. We identify each differential monomial with its colored multiplicity and analyse our computation in the light of the free differential calcu- lus. We propose also a combinatorial interpretation of coefficients of (Gk). These coefficients are powers of an operator Θ which is in the monoid generated by two linear differential operators ∆ and Γ. More than a symbolic validation, these computing tools are param- eterized by the input and the system's behavior.
Origine : Fichiers produits par l'(les) auteur(s)
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