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Some basic results on M-matrices in connection with the Accelerated Overrelaxation (AOR) method

Einige Grundresultate über M-Matrizen im Zusammenhang mit der Methode der beschleunigten Überrelaxation (AOR)

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Abstract

This paper extends some recent results by Varga concerning the theory of M-matrices, in connection with the well known iterative methods of Jacobi, of Extrapolated Jacobi and of Successive Over-relaxation, in two directions: i) The iteration matrix of the iterative scheme considered is more general than that of the aforementioned methods and may include a diagonal part and ii) the theory is presented in such a way that the number of equivalent statements given in the text covers the Accelerated Overrelaxation (AOR) method introduced by the present author not long ago.

Zusammenfassung

Die vorliegende Arbeit erweitert einige neue Resultate von Varga bezüglich der Theorie derM-Matrizen in Zusammenhang mit den wohlbekannten iterativen Methoden von Jacobi, des extrapolierten Jacobi und der sukzessiven Überrelaxation, in zwei Richtungen: i) Die Iterationsmatrix des iterativen Schemas ist allgemeiner als die der obengenannten Methoden und kann einen Diagonalteil enthalten; ii) Die Theorie ist so dargestellt, daß die äquivalenten Aussagen die Methode der beschleunigten Überrelaxation (AOR), die vom gegenwärtigen Autor vor kurzem eingeführt wurde, mit enthalten.

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Authors and Affiliations

  1. Department of Mathematics, University of Ioannina, Ioannina, Greece

    A. Hadjidimos

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  1. A. Hadjidimos
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Hadjidimos, A. Some basic results on M-matrices in connection with the Accelerated Overrelaxation (AOR) method. Computing 24, 259–268 (1980). https://doi.org/10.1007/BF02281730

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  • DOI: https://doi.org/10.1007/BF02281730

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