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arXiv · 1306.1136

Interval systems over idempotent semiring

Laurent Hardouin·Bertrand Cottenceau·Mehdi Lhommeau·Euriell Le Corronc
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Abstract

This paper deals with solution of inequality $\textbf{A}\otimes \textbf{x}\preceq \textbf{b}$, where $\textbf{A}, \textbf{x}$ and $\textbf{b}$ are interval matrices with entries defined over idempotent semiring. It deals also with the computation of a pair of intervals, ($\textbf{x},\textbf{y}$) which satisfies the equation $\textbf{A} \otimes \textbf{x}=\textbf{B}\otimes \textbf{y}$. It will be shown that this equation may be solved by considering the interval version of the iterative scheme proposed by Cuninighame-Green and Butkovic in 2003.

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Laurent Hardouin, Bertrand Cottenceau, Mehdi Lhommeau, Euriell Le Corronc. 2013-06-05. Interval systems over idempotent semiring. https://doi.org/10.1016/j.laa.2009.03.039

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