On the speed of convergence of the total step iterative method for a class of interval linear algebraic systems (Q676169)

Systems of linear interval equations of the form \(x=Ax+b\) are considered. It is well-known that the total step method applied to such a system converges to a fixed point \(x^*\) (being then an interval vector) iff \(\rho (|A|)\), that is the spectral radius of \(|A |\) is smaller than 1, and further, that \(\alpha_T\leq \rho(|A|)\) where \(\alpha_T\) denotes the asymptotic convergence factor for the total step method w.r. to the system \(x=A x+b\) and \(x^*\) [cf. \textit{G. Alefeld} and \textit{J. Herzberger}, Introduction to interval computations (1983; Zbl 0552.65041)]. -- In the paper it is shown that even \(\alpha_T= \rho(|A|)\) holds when \(0\notin a_{ij}\) and \(0\in b_i\) is assumed.