# Regularity of Interval Matrices and Theorems of the Alternatives

Regularity of Interval Matrices and Theorems of the Alternatives We give several characterizations of regularity of interval matrices. All of them have to do with solvability of certain systems of nonlinear equations or inequalities. The most illustrative of them is the following one: an interval matrix [A c − Δ, A c + Δ] is regular if and only if the nonlinear inequality \$\$|x| > \Delta |A_{c}^{-1}x|\$\$ has a solution in each orthant. These results are then applied to derive two theorems of the alternatives for inequalities with absolute values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Regularity of Interval Matrices and Theorems of the Alternatives

, Volume 12 (2) – Jan 1, 2006
7 pages

/lp/springer_journal/regularity-of-interval-matrices-and-theorems-of-the-alternatives-ljCR3O4zPW
Publisher
Springer Journals
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/s11155-006-4877-z
Publisher site
See Article on Publisher Site

### Abstract

We give several characterizations of regularity of interval matrices. All of them have to do with solvability of certain systems of nonlinear equations or inequalities. The most illustrative of them is the following one: an interval matrix [A c − Δ, A c + Δ] is regular if and only if the nonlinear inequality \$\$|x| > \Delta |A_{c}^{-1}x|\$\$ has a solution in each orthant. These results are then applied to derive two theorems of the alternatives for inequalities with absolute values.

### Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

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