Optimal Finite Characterization of Linear Problems with Inexact Data

Optimal Finite Characterization of Linear Problems with Inexact Data 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Optimal Finite Characterization of Linear Problems with Inexact Data

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-0406-8
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

References

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