Improved enclosure for some parametric solution sets with linear shape

Consider linear algebraic systems where the elements of the matrix and the right-hand side vector depend linearly on a number of interval parameters. We prove some sufficient conditions for the united parametric solution set of such a system to have linear boundary. These conditions imply an equivalent representation of the parametric system where each parameter appears once in a diagonal matrix. The latter representation allows us to expand the scope of applicability of the best known so far interval method, developed by A. Neumaier and A. Pownuk, for enclosing the parametric solution set and to generalize the method for systems where the parameter dependencies connect the matrix and the right-hand side vector. Some examples demonstrate that: parametric solution sets with linear boundary appear in various application domains, the generalized method improves the solution enclosure and the proven sufficient conditions can be helpful for solving various other interval problems.