Computing Exact Bounds on Elements of an Inverse Interval Matrix is NP-Hard
- Cite this article as:
- Coxson, G.E. Reliable Computing (1999) 5: 137. doi:10.1023/A:1009901405160
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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.