Diskrete Approximation von Eigenwertproblemen

1. Einleitung Die Existenz asymptotischer Entwicklungen kann bei vieIen numerischen Verfahren sehr vorteilhaft ausgenutzt werden. Die auf [16, 4] zurfickgehende Idee hat z.B. mit der Romberg-Integration (s. L9, t0]) und mit dem Verfahren von Gragg-Bulirsch-Stoer [2, 3] bei gew6hnlichen Anfangswertaufgaben zur Aufstellung ~uBerst wirkungsvoller numerischer Prozeduren geftihrt. Ftir eine Ubersicht vgl. die Arbeiten [t0, t9]. Die vorliegende Arbeit besch~ftigt sich in einem allgemeinen Rahmen mit der Existenz asymptotischer Entwicklungen ftir die Eigenwerte und Hauptvektoren bei der n~herungsweisen L/~sung des Eigenwertproblems

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