Abstract
We introduce iterative methods for systems of equations with interval coefficients and linear form by suitable matrix splittings. When compared to the iterative methods for systems amenable to iteration introduced in [1], improved convergence and inclusion properties can be proved under suitable conditions. The method can also be used in the solution of specific nonlinear systems of equations by interval arithmetic methods.
Zusammenfassung
Für Gleichungssysteme mit Intervallkoeffizienten und linearer Gestalt werden mittels geeigneter Matrixzerlegungen Iterationsverfahren eingeführt, die unter geeigneten Voraussetzungen im Vergleich zu den in [1] beschriebenen Verfahren für Gleichungssysteme in iterationsfähiger Gestalt verbesserte Konvergenzund Einschließungseigenschaften besitzen. Die Verfahren können auch im Rahmen der Lösung bestimmter nichtlinearer Gleichungssysteme mittels intervallarithmetischer Mittel verwendet werden.
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Schwandt, H. Iterative methods for systems of equations with interval coefficients and linear form. Computing 38, 143–161 (1987). https://doi.org/10.1007/BF02240179
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DOI: https://doi.org/10.1007/BF02240179