On the Symmetric and Unsymmetric Solution Set of Interval Systems

Abstract

We consider the solution set $S$ of real linear systems $Ax = b$ with the $n \times n$ coefficient matrix $A$ varying between a lower bound $\underline{A}$ and an upper bound $\overline{A}$, and with $b$ similarly varying between $\underline{b}, \overline{b}$. First we list some properties on the shape of $S$ if all matrices $A$ are nonsingular. Then we restrict $A$ to be nonsingular and symmetric deriving a complete description for the boundary of the corresponding symmetric solution set $S_{\rm sym}$ in the $2 \times 2$ case. Finally we derive a new criterion for the feasibility of the Cholesky method with which bounds for $S_{\rm sym}$ can be found.