# Computing Exact Bounds on Elements of an Inverse Interval Matrix is NP-Hard

Computing Exact Bounds on Elements of an Inverse Interval Matrix is NP-Hard For a given interval matrix, it would be valuable to have a practical method for determining the family of matrices which are inverses of its members. Since the exact family of inverse matrices can be difficult to find or to describe, effort is often applied to developing methods for determining matrix families with interval structure which "best" approximate or contain it. A common approach is to seek exact bounds on individual elements. In this paper, we show that computing exact bounds is NP-hard; therefore any algorithm will have at least exponential-time worst-case computational cost unless P = NP. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Computing Exact Bounds on Elements of an Inverse Interval Matrix is NP-Hard

, Volume 5 (2) – Sep 30, 2004
6 pages

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
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.
10.1023/A:1009901405160
Publisher site
See Article on Publisher Site

### Abstract

For a given interval matrix, it would be valuable to have a practical method for determining the family of matrices which are inverses of its members. Since the exact family of inverse matrices can be difficult to find or to describe, effort is often applied to developing methods for determining matrix families with interval structure which "best" approximate or contain it. A common approach is to seek exact bounds on individual elements. In this paper, we show that computing exact bounds is NP-hard; therefore any algorithm will have at least exponential-time worst-case computational cost unless P = NP.

### Journal

Reliable ComputingSpringer Journals

Published: Sep 30, 2004

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