Abstract
By exploiting generalized error-bounds for the well-known hyperpower methods for approximating the inverse of a matrix we derive inclusion methods for the inverse matrix. These methods make use of interval operations in order to give guaranteed inclusions whenever the convergence of the applied hyperpower method can be shown. The efficiency index of some of the new methods is greater than that of the optimal methods in [2] or [5]. A numerical example is given.
Zusammenfassung
Durch Auswertung von verallgemeinerten Fehlerschranken für Hyperpower Methoden zur näherungsweisen Berechnung der Inversen einer Matrix erhalten wir Einschließungsalgorithmen für die inverse Matrix. Unsere Verfahren verwenden Intervallverknüpfungen zur Gewinnung garantierter Einschließungen, wann immer die Konvergenz der verwendeten Hyperpower Methode gezeigt werden kann. Der Effizienzindex einiger dieser neuen Verfahren ist größer als jener der optimalen Verfahren in [2] oder [5]. Ein numerisches Beispiel wird gegeben.
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Dedicated to Professor Dr. J. W. Schmidt on the occasion of his 60th birthday
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Herzberger, J. Efficient algorithms for the inclusion of the inverse matrix using error-bounds for hyperpower methods. Computing 46, 279–288 (1991). https://doi.org/10.1007/BF02257773
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DOI: https://doi.org/10.1007/BF02257773