An asymptotic result for linear interval systems (Q1121633)

The author expands the bounds \(\underline{x},\bar x\in {\mathbb{R}}^ n\) of the interval hull of the solution set \(X=\{x';A'x'=b'\), \(A'\in A^ I\in I{\mathbb{R}}^{n\times n}\), \(b'\in b^ I\in I{\mathbb{R}}^ n\}\) into an infinite series. To this end he uses the diagonal entries of some recursively defined matrices. For small diameters of \(A^ I\) and \(b^ I\) he deduces asymptotic expressions for \b{x}, \(\bar x\) improving an estimate for the radius of \([\underline{x},\bar x]\) due to \textit{W. Miller} [ibid. 12, 213-219 (1972; Zbl 0242.65034)].