Centered Solutions for Uncertain Linear Equations

Abstract

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex.We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of uncertain linear equations, we compute the maximum size inscribed convex body (MCB) of the set of all possible solutions. The obtained MCB is an inner approximation of the solution set, and its center is a potential solution to the system. We compare our method both theoretically and numerically with an existing method that minimizes the worst-case violation. Applications to the input-output model, Colley's Matrix Rankings and Article Influence Scores demonstrate the advantages of the new method.

Keywords: Interval linear systems; uncertain linear equations; maximum volume inscribed ellipsoid

JEL Classification: C61