Relations between various methods for solving linear interval and parametric equations

Abstract

In the first part of the paper, we consider standard systems of linear interval equations and we focus particularly on two solution methods, the Bauer–Skeel method and the Hansen–Bliek–Rohn method. We show relations between these two methods and between various modifications that are based on preconditioning of the system and on the residual form. We compare as well the quality of the bounds produced by the different variants and we show that for some variants, the Bauer–Skeel bounds naturally arise from other approaches such as Krawczyk of Jacobi iterations, too. In the second part of the paper, we consider interval parametric linear systems with affine-linear dependencies. We also investigate various forms of enclosures, and we not only compare them with each other, but we also show relations to some already known methods. As a consequence, we come up with novel and interesting relations between several algorithms.