THE SHAPE OF THE SOLUTION SET FOR SYSTEMS OF INTERVAL LINEAR-EQUATIONS WITH DEPENDENT COEFFICIENTS

A standard system of interval linear equations is defined by Ax = b, w here A is an m x n coefficient matrix with (compact) intervals as entr ies, and b is an m-dimensional vector whose components are compact int ervals. It is known that for systems of interval linear equations the solution set, i.e., the set of all vectors a for which Ax = b for some A is an element of A and b is an element of b, is a polyhedron. In so me cases, it makes sense to consider not all possible A is an element of A and b is an element of b, but only those A and b that satisfy cer tain linear conditions describing dependencies between the coefficient s. For example, if we allow only symmetric matrices A (a(ij) = a(ji)), then the corresponding solution set becomes (in general) piecewise-qu adratic. In this paper, we show that for general dependencies, we can have arbitrary (semi)algebraic sets as projections of solution sets.