On a theorem of Stein-Rosenberg type in interval analysis (Q1089728)

For real \(n\times n\) interval matrices A with irreducible upper bound and nonnegative lower bound the asymptotic convergence factor \(\alpha_ T\) of the total step method \(x^{m+1}=Ax^ m+b\) is compared with the factor \(\alpha_ S\) of the corresponding single step method. Extending results given in another paper of the author [Linear Algebra Appl. 85, 153-164 (1987; reviewed below)] he obtains a theorem similar to parts of the classical theorem of Stein and Rosenberg, see for instance \textit{R. Varga} [Matrix iterative analysis (1963; Zbl 0133.086)].