Proving endpoint dependence in solving interval parametric linear systems

Linear algebraic systems involving linear dependencies between interval valued parameters and the so-called united parametric solution set of such systems are considered. The focus is on systems, such that the vertices of their interval hull solution are attained at particular endpoints of some or all parameter intervals. An essential part of finding this endpoint dependence is an initial determination of the parameters which influence the components of the solution set, and of the corresponding kind of monotonicity. In this work, we review a variety of interval approaches for the initial monotonicity proof and compare them with respect to both computational complexity and monotonicity proving efficiency. Some quantitative measures are proposed for the latter. We present a novel methodology for the initial monotonicity proof, which is highly efficient from a computational point of view, and which is also very efficient to prove the monotonicity, for a wide class of interval linear systems involving parameters with rank 1 dependency structure. The newly proposed method is illustrated on some numerical examples and compared with other approaches.