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Comptes Rendus. Mathématique
Numerical Analysis
A functional equation with polynomial solutions and application to Neural Networks
Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1059-1072.

We construct and discuss a functional equation with contraction property. The solutions are real univariate polynomials. The series solving the natural fixed point iterations have immediate interpretation in terms of Neural Networks with recursive properties and controlled accuracy.

Published online:
DOI: 10.5802/crmath.124
Classification: 65Q20,  65Y99,  78M32
Bruno Després 1; Matthieu Ancellin 2

1 Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France and Institut Universitaire de France, France
2 Université Paris-Saclay, ENS Paris-Saclay, CNRS, Centre Borelli, F-91190 Gif-sur-Yvette, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Bruno Despr\'es and Matthieu Ancellin},
     title = {A functional equation with polynomial solutions and application to {Neural} {Networks}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1059--1072},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {9-10},
     year = {2020},
     doi = {10.5802/crmath.124},
     language = {en},
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Bruno Després; Matthieu Ancellin. A functional equation with polynomial solutions and application to Neural Networks. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1059-1072. doi : 10.5802/crmath.124. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.124/

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