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Title: Free (rational) derivation
Authors: Schrempf, K.
Keywords: Hausdorff derivative;Free associative algebra;Free field;Minimal linear representation;Admissible linear system;Free fractions;Chain rule;Newton iteration;Derivada de Hausdorff;Álgebra asociativa libre;Campo libre;Representación lineal mínima;Sistema lineal admisible;Fracciones libres;Regla de la cadena;Iteración de Newton
Issue Date: 2021
Publisher: Universidad de Extremadura
Abstract: By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer’s linear representations, we provide an algorithmic construction for the (partial) non-commutative (or Hausdorff-) derivative and show how it can be applied to the non-commutative version of the Newton iteration to find roots of matrix-valued rational equations.
DOI: 10.17398/2605-5686.36.1.25
Appears in Collections:Extracta Mathematicae Vol. 36, nº 1 (2021)

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