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Interval solutions of linear interval equations. (English) Zbl 0716.65047
We use the notations of the preceding review. Let a nonsingular interval matrix \(A^ I\) be given by the \(n\times n\) matrices \(A^-=(a^- _{ij})\) and \(A^+=(a^+_{ij})\), and similarly the interval vector \(b^ I=[b^-,b^+]\) by \(b^-=(b^-_ i)\), \(b^+=(b^+_ i)\in {\mathbb{R}}^ n\). The problem of finding an interval n-vector solution \(x^ I=[x^-,x^+]\) of \[ (*)\;\sum^{n}_{j=1}[a^- _{ij},a^+_{ij}]\cdot [x^-_ j,x^+_ j]=[b^-_ i,b^+_ i],\;i=1,...,n, \] is considered under the additional assumption that there exist \(A',A''\in A^ I\) and \(x',x''\in x^ I\) such that \(A'x'=b^-\) and \(A''x''=b^+\) hold. The solvability of this problem is related to solving the equations \(A_ cx-\Delta (| x_ j|)=b^-\) and \(A_ cx+\Delta (| x_ j|)=b^+\). The unique solutions of these two equations are utilized to obtain an algorithm to find a solution of the above type for (*) or alternatively to confirm that no such solution exists.
Reviewer: M.Kracht

MSC:
65G30 Interval and finite arithmetic
65F30 Other matrix algorithms (MSC2010)
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