On Symmetric Solution Sets

Given an n x n interval matrix [A] and an interval vector [b] with n components we present an overview on existing results on the solution set S of linear systems of equations Ax=b with symmetric matrices A from [A] and vectors b from [b]. Similarly we consider the set E of eigenpairs associated with the symmetric matrices A from [A]. We report on characterizations of S by means of inequalities, by means of intersection of sets, and by an approach which is generalizable to more general dependencies of the entries. We also recall two methods for enclosing S by means of interval vectors, and we mention a characterization of E