Optimal Finite Characterization of Linear Problems with Inexact Data

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2004

Comments

UTEP-CS-00-37b.

Published in Reliable Computing, 2005, Vol. 11, No. 6, pp. 479-489.

Abstract

For many linear problems, in order to check whether a certain property is true for all matrices A from an interval matrix [A], it is sufficient to check this property for finitely many "vertex" matrices. J. Rohn has discovered that we do not need to use all 2^(n^2) vertex matrices, it is sufficient to only check these properties for 2^(2n-1)<<2^(n^2) vertex matrices of a special type A_{yz}. In this paper, we show that a further reduction is impossible: without checking all 2^(2n-1) matrices A_{yz}, we cannot guarantee that the desired property holds for all A from [A]. Thus, these special vertex matrices provide an optimal finite characterization of linear problems with inexact data.