On the solution sets of particular classes of linear interval systems

Abstract

We characterize the solution set S of real linear systems Ax= b by a set of inequalities if b lies between some given bounds b ̄ , b ̄ and if the n× n coefficient matrix A varies similarly between two bounds A̱ and Ā. In addition, we restrict A to a particular class of matrices, for instance the class of the symmetric, the skew-symmetric, the persymmetric, the Toeplitz, and the Hankel matrices, respectively. In this way, we generalize the famous Oettli–Prager criterion (Numer. Math. 6 (1964) 405), results by Hartfiel (Numer. Math. 35 (1980) 355) and the contents of the papers (in: R.B. Kearfott, V. Kreinovich (Eds.), Applications of Interval Computations, Kluwer, Boston, MA, 1996, pp. 61–79) and (SIAM J. Matrix Anal. Appl. 18 (1997) 693).