On the applicability of the interval Gaussian algorithm (Q1276141)

Let a system of linear interval equations, \(Ax =b\), be given where \(A\) is of the special form \(A= I +[-R,R]\) and regular, \(I\) is the identity matrix and \(R\) is a matrix with nonnegative real entries. The application of the interval Newton algorithm is investigated. The authors call the algorithm applicable to the system if no division through zero occurs during the computation so that a finite solution \(x_G\) is obtained. Now, necessary and sufficient conditions for the system are derived that the algorithm is applicable. Then it is shown that each component of \(x_G\), which is an interval vector has an endpoint which is optimum.