Taiwanese Journal of Mathematics

ABOUT SUCCESSIVE GAUSS-SEIDELISATIONS

Philippe Poncet and Francois Robert

Full-text: Open access

Abstract

This note addresses 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 problem remains still open for $n\geq 4$.

Article information

Source
Taiwanese J. Math., Volume 3, Number 4 (1999), 491-501.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407162

Digital Object Identifier
doi:10.11650/twjm/1500407162

Mathematical Reviews number (MathSciNet)
MR1730983

Zentralblatt MATH identifier
0945.39009

Subjects
Primary: 15A18: Eigenvalues, singular values, and eigenvectors 34C35 34DXX

Keywords
discrete operator Gauss-Seidel operator computer algebra boolean algebra gr\"obner basis $n$-cube graph theory short cycled transformation

Citation

Poncet, Philippe; Robert, Francois. ABOUT SUCCESSIVE GAUSS-SEIDELISATIONS. Taiwanese J. Math. 3 (1999), no. 4, 491--501. doi:10.11650/twjm/1500407162. https://projecteuclid.org/euclid.twjm/1500407162


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