Abstract
We present new methods for solving special classes of linear interval equations by means of suitable selection systems. First we prove some theorems characterizing the extremal points of the solution set. For invers-stable interval matrices and systems whose solution set are contained in one orthant we give algorithms to select such systems the solutions of which generate the interval hull.
Zusammenfassung
Vorgestellt werden neue Methoden zur Lösung spezieller Klassen linearer Intervallgleichungssysteme mittels geeigneter Auswahlsysteme. Zuerst beweisen wir einige Sätze die die Extremalpunkte der Lösungsmenge charakterisieren. Für invers stabile Matrizen sowie für Systeme, deren Lösungen nur in einem Orthanten liegen, werden Algorithmen für die Auswahl solcher Gleichungen angegeben, deren Lösungen die Intervallhülle erzeugen.
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References
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Rohn, J.: Solving interval linear systems. Freiburger Intervall-Berichte84/7, 1–14
Rohn, J.: Formulae for exact bounds on solutions of linear systems with rank one perturbations. Freiburger Intervall-Berichte87/6, 1–20
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Hudak, D. On the determination of the interval hull of linear interval equations. Computing 46, 253–263 (1991). https://doi.org/10.1007/BF02238301
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DOI: https://doi.org/10.1007/BF02238301