Computing the Cube of an Interval Matrix is NP-Hard

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Guenter Mayer
Hung T. Nguyen

Publication Date

11-2004

Comments

UTEP-CS-04-28a.

Published in Proceedings of the 2005 ACM Symposium on Applied Computing, Santa Fe, New Mexico, March 13-17, 2005, pp. 1449-1453.

Abstract

In many practical applications, we are interested in computing the product of given matrices and/or a power of a given matrix. In some cases, the initial matrices are only known with interval uncertainty. It turns out that under this uncertainty, there is a principal difference between the product of two matrices and the product of three (or more) matrices:

on the one hand, it is more or less known that the problems of computing the exact range for the product of two matrices -- and for the square of a matrix -- are computationally feasible;

on the other hand, we prove that the problems of computing the exact ranges for the product of three matrices -- and for the third power of a matrix -- are NP-hard.