Solvability of Parametric Interval Linear Systems of Equations and Inequalities
Evgenija D. Popova · SIAM Journal on Matrix Analysis and Applications · 2015
Considered are linear algebraic systems of equations and/or inequalities involving linear dependencies between interval-valued parameters. The goal is to characterize weak and strong solvability of such systems. Since any parametric interval equation is equivalent to a system of parametric interval inequalities, the focus is on the latter. We discuss an algorithmic procedure for characterizing the weak solutions, and thus weak solvability, of the considered systems. The set of strong solutions to a mixed system of parametric interval equations and inequalities is described explicitly. Applying the theory of weak solvability of parametric interval systems, we prove necessary and sufficient conditions for strong solvability of parametric interval inequalities.