Balanced Random and Adaptive Interval Arithmetic for Systems of Linear Interval Equations

Abstract

The paper concerns interval methods — valuable tools for solving engineering problems — for finding outer approximations for the solution set of systems of linear interval equations. The paper shows how interval methods are used to analyse steady-state concentrations of systems of coupled reactors. The results of the experiments evaluating the outer approximations for the solution set of systems of linear interval equations using Gaussian elimination with standard and balanced random interval arithmetic are given. Adaptive interval arithmetic is proposed to overcome disadvantages of balanced random interval arithmetic.