Solvability of linear Interval System of Equations via Oettli-Prager Theorem and Rohn’s bound

Abstract

In general, numerical results computed by interval methods tend to grow in diameters as a result of data dependencies and cluster effects which may be traced to error from one source that can affect every other source and thereby drastically lower the efficiency of the interval inclusion methods. We describe in this paper how this can be reduced and an attempt is made to address the above problems subject to tolerable solution sets. Basic computational tools at our disposal are the Oettli-Prager’s theorem and Rohn’s method which combine floating point operation with an interval method.

Keywords : linear interval systems of equations, hull of solution set of linear interval systems, Oettli-Prager theorem, Bauer-Skeel bounds