Diagrammatic analysis of interval linear equations. II: The two-dimensional case and generalization to \(n\) dimensions
This very interesting paper is devoted to the diagrammatic analysis of interval linear equations. The author uses the results obtained for the one-dimensional case, as it is described in Part I [Reliab. Comput. 9, No. 1, 1--20 (2003; Zbl 1071.15002)] of the study published in the same journal, recently. It is extended to the two-dimensional relational expression denoted by \(a_1\cdot x_1+a_2\cdot x_2\diamondsuit b\), where \(\diamondsuit \in \{\eqcirc,\supseteq , \subseteq , = \}\). An analysis is established by a midpoint-radius diagram, and then generalized to the \(n-\)dimensional expression \(\sum_{i=1}^{n}a_i\cdot x_i\diamondsuit b\). The solution sets are obtained with a simple boundary-line selection rule derived using these tools, and are characterized by types of one-dimensional cuts through the solution space. A classification of basic possible solution types is provided in detail. The generalization of the approach for \(n-\)dimensional interval systems is also discussed.
scientific article; zbMATH DE number 1960155