Solvability of systems of linear interval equations. (English) Zbl 1061.15003

Summary: A system of linear interval equations is called solvable if each system of linear equations contained therein is solvable. In the main result of this paper it is proved that solvability of a general rectangular system of linear interval equations can be characterized in terms of nonnegative solvability of a finite number of systems of linear equations which, however, is exponential in matrix size; the problem is proved to be NP-hard. It is shown that three earlier published results are consequences of the main theorem, which is compared with its counterpart valid for linear interval inequalities that turn out to be much less difficult to solve.


15A06 Linear equations (linear algebraic aspects)
15A39 Linear inequalities of matrices
65G30 Interval and finite arithmetic
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