Topics in matrix analysis
Solving the linear interval tolerance problem
Mathematics and Computers in Simulation
On the Approximation of Linear AE-Solution Sets
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
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We consider a linear algebraic system A(p)x=b(q), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. The linear tolerance problem for the so-called parametric tolerable solution set @S"t"o"l(A(p),b(q),[p],[q])={x@?R^n|(@?p@?[p])(@?q@?[q])(A(p)x=b(q))} requires an inner estimation of this solution set, that is an interval vector [y], such that [y]@?@S"t"o"l(A(p),b(q),[p],[q]). In this paper we consider the first methods for finding inner estimation of the parametric tolerable solution set, namely, we propose parametric generalization of the so-called centered approach and of the vertex approach. The results obtained by the two approaches are compared on some numerical examples. The advantages of the parametric approach are demonstrated on problems with independent nonparametric entries and in controllability analysis of linear dynamical systems involving interval uncertainties.