About Successive Gauss-Seidelisations

Philippe Poncet (1) , François Robert (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ENSIMAG - École nationale supérieure d'informatique et de mathématiques appliquées

This note adresses the general problem of the dynamical behavior for successive Gauss-Seidel transformations (shortly called Gauss-Seidelisations) of a given mapping over the n-cube. Complete results are given for n = 2 and n = 3, and then a natural conjecture is proved to be false for greater n. Thus this interesting and simple problem remains still open for n ≥ 4.

Mots clés: Gröbner basis; Boolean algebra; Computer algebra; Gauss-Seidel; Discrete Operators; Short cycled transformations; n-cube-Graph theory

Domaines: Informatique [cs]; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]; Combinatoire [math.CO]

Philippe Poncet, François Robert. About Successive Gauss-Seidelisations. Taiwanese Journal of Mathematics, TJM, 1999, 3, pp.491 - 501. ⟨10.11650/twjm/1500407162⟩. ⟨hal-02010704⟩