Solving the Tolerance Problem for Interval Linear Systems
نویسنده
چکیده
For the interval linear system Ax = b, we consider the linear tolerance problem, requiring inner evaluation of the tolerable solution set Σ∀∃(A,b) = {x∈ R|(∀A∈A)(Ax∈b)} formed by all point vectors x such that the product Ax remains within b for all possible A∈A. We develop solvability theory for the linear tolerance problem that not only settles whether Σ∀∃ is empty or not, but also enables modification of the problem to ensure its desired properties. The paper concludes with a survey of new methods for construction of an interval solution to the linear tolerance problem around a given center.
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