Abstract
Different solution sets for the interval system A · x = b are characterized and classified using diagrammatic tools for interval analysis developed recently. A thorough analysis of the basic, one-dimensional system a · x ◊ b is conducted, with the help of a MR-diagram, in which all the needed relations ◊ ∈ {\(\mathop o\limits_ - ^ - \), ⊇, ⊆,=} are directly representable. The solution sets are obtained with simple diagrammatic constructions, in terms of quotients of a and b. A complete classification of all possible solution types is provided as a result. The generalization of the analysis to 2- and n-dimensional systems is outlined as well.
The paper was supported by the Research Project No. 8 T11 F 006 15 (for the years 1998–2001) from KBN (The State Committee for Scientific Research).
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Kulpa, Z. (2001). Towards Diagrammatic Analysis of Systems of Interval “Linear Equations”. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_10
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_10
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