# Solving interval linear systems with linear programming techniques

Solving interval linear systems with linear programming techniques In this paper, we show how it is possible to use convex polyhedra for solving linear interval systems without using preconditioning. We first show how to derive, from an enclosure of □ Σ (( A ), ( b )), a polyhedron which contains the convex hull of the solution set. Then, a simplex-like method enables us to find a new outer inclusion. Moreover, the constraints obtained may be used to compute an inner inclusion of □ Σ (( A ), ( b )). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Linear Algebra and its Applications Elsevier

# Solving interval linear systems with linear programming techniques

17 pages

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### Abstract

In this paper, we show how it is possible to use convex polyhedra for solving linear interval systems without using preconditioning. We first show how to derive, from an enclosure of □ Σ (( A ), ( b )), a polyhedron which contains the convex hull of the solution set. Then, a simplex-like method enables us to find a new outer inclusion. Moreover, the constraints obtained may be used to compute an inner inclusion of □ Σ (( A ), ( b )).

### Journal

Linear Algebra and its ApplicationsElsevier

Published: Sep 15, 1998

### References

• Checking bounds on solutions of linear interval equation is NP-hard
Rohn, J.

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