Interval systems over idempotent semiring

TL;DR

This paper explores solving inequalities and equations involving interval matrices over idempotent semirings, extending iterative methods to handle interval data for more robust solutions.

Contribution

It introduces methods for solving inequalities and equations with interval matrices over idempotent semirings, adapting existing iterative schemes for interval data.

Findings

Solution of inequalities using interval matrices over idempotent semirings

Extension of iterative schemes to interval data

Effective computation of interval solutions for matrix equations

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.