Visualization of Parametric Solution Sets

Evgenija D. Popova

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

We discuss the characterization and visualization of the solution sets to the following classes of interval linear systems:

The well-known Oettli-Prager theorem (and its generalization for quantified intervals) characterizes the solution set of an interval linear system, where all interval entries are assumed to be independent, by a set of algebraic inequalities. This characterization and a Mathematica package `InequalityGraphics` are utilized by an updated function from the package IntervalComputations`SolutionSets` for 2D and 3D visualization of both classes nonparametric solution sets - the united solution set and the so-called AE-solution sets.

In case of linear systems whose entries depend on interval parameters we propose a new characterization of the parametric solution set by means of parametric hypersurfaces. Based on this approach, a bounded parametric solution set can be visualized by its boundaries, which are pieces of particular parametric hypersurfaces. Computer algebra systems Mathematica and Maple provide tools for easy implementation of this approach.

An expansion of the Mathematica package IntervalComputations`SolutionSets` will be reported. Numerous examples of both the united (parametric) solution set and the (parametric) AE-solution sets will demonstrate the visualization tools and the properties of the solution sets.