On the solution sets of particular classes of linear interval systems

Authors:
Götz Alefeld;Vladik Kreinovich;Günter Mayer
Affiliations:
Institut für Angewandte Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany;Department of Computer Science, University of Texas at El Paso, El Paso, TX;Fachbereich Mathematik, Universität Rostock, Universitatsplatz 1, D-18051 Rostock, Germany
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

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Abstract

We characterize the solution set S of real linear system 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 A and A. 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).