INNER ESTIMATION OF LINEAR PARAMETRIC AE-SOLUTION SETS

We consider linear algebraic systems A(p)x = b(p), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. For the parametric AE-solution set defined for two disjoint index sets A, E by Sigma(p)(AE) := {x is an element of R-n vertical bar (for all p(A) is an element of [p(A)]) (there exists p(epsilon) is an element of [p(epsilon)])(A(p)x = b(p))}, an inner interval estimation [y] subset of Sigma(p)(AE) is sought. In the special case when Sigma(p)(AE) has linear shape, this paper gives parametric generalization of the so-called centred approach, which was developed so far only for tolerable solution sets.