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 A ∈ A. J. Rohn has discovered that we do not need to use all 2n 2 vertex matrices, it is sufficient to only check these properties for 22n−1 ≪ 2n 2 vertex matrices of a special type Ayz. In this paper, we show that a further reduction is impossible: without checking all 22n−1 matrices Ayz, we cannot guarantee that the desired property holds for all A ϵ A. Thus, these special vertex matrices provide an optimal finite characterization of linear problems with inexact data.
Reliable Computing – Springer Journals
Published: Jan 1, 2005
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