Algebraic approach in the “outer problem” for interval linear systems

The subject of our work is the classical “outer” problem for the interval linear algebraic system $\mathbf{A}x=\mathbf{b}$ with the interval matrix $\mathbf{A}$ and right-hand side vector $\mathbf{b}$: find “outer” coordinate-wise estimates of the solution set formed by all solutions to the point systems $Ax=b$ with $A\in\mathbf{A}$ and $b\in\mathbf{b}$. The purpose of this work is to propose a new algebraic approach to the above problem, in which it reduces to solving one point (noninterval) equation in the Euclidean space of the double dimension. We construct a specialized algorithm (subdifferential Newton method) that implements the new approach, present results of its numerical tests. They demonstrate that the algebraic approach combines exclusive computational efficacy with high quality enclosures of the solution set.