Abstract
We describe an algorithm with which one can verify solutions of an additive inverse matrix eigenvalue problem. The algorithm is based on Newton's method using a new criterion for terminating the iteration. In addition, it yields tight interval bounds for the solutions of the problem, thus guaranteeing most of their leading digits in a given floating point system.
Zusammenfassung
Wir geben einen Algorithmus an, mit dem man Lösungen eines additiven inversen Matrizen-Eigenwertproblems nachweisen kann. Der Algorithmus beruht auf dem Newton-Verfahren, für das ein neues Abbruchkriterium verwendet wird. Er liefert enge Schranken für die Lösungen des Problems und garantiert so die meisten ihrer führenden Ziffern in einem gegebenem Gleitpunktsystem.
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We thank the Deutsche Forschungsgemeinschaft (‘DFG’) for supporting this work under grant Al 175/4-1 and Al 175/4-2.
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Alefeld, G., Gienger, A. & Mayer, G. Numerical validation for an inverse matrix eigenvalue problem. Computing 53, 311–322 (1994). https://doi.org/10.1007/BF02307382
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DOI: https://doi.org/10.1007/BF02307382