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http://hdl.handle.net/10662/12299
| 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. |
| URI: | http://hdl.handle.net/10662/12299 |
| DOI: | 10.17398/2605-5686.36.1.25 |
| Appears in Collections: | Extracta Mathematicae Vol. 36, nº 1 (2021) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2605-5686_36_1_25.pdf | 564,41 kB | Adobe PDF | View/Open |
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