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On the R-order of coupled sequences III

Über die R-Ordnung gekoppelter Folgen III

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Abstract

For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).

Zusammenfassung

Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.

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References

  1. Burmeister, W., Schmidt, J. W.: On theR-order of coupled sequences II. Computing29, 73–81 (1982).

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  2. Ortega, J. M., Rheinboldt, W. C.: Iterative solution of nonlinear equations in several variables. New York-London: Academic Press 1970.

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  3. Schmidt, J. W.: On theR-order of coupled sequences. Computing26, 333–342 (1981).

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  4. Schwetlick, H.: Numerische Lösung nichtlinearer Gleichungen. Berlin: Deutscher Verlag der Wissenschaften 1979.

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Authors and Affiliations

  1. Institut für Mathematik, Akademie der Wissenschaften, Mohrenstrasse 39, DDR-1080, Berlin, German Democratic Republic

    W. Burmeister

  2. Sektion Mathematik, Technische Universität, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    J. W. Schmidt

Authors
  1. W. Burmeister
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  2. J. W. Schmidt
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Additional information

Part I in Computing26, 333–342 (1981), part II in Computing29, 73–81 (1982).

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Burmeister, W., Schmidt, J.W. On the R-order of coupled sequences III. Computing 30, 157–169 (1983). https://doi.org/10.1007/BF02280786

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  • DOI: https://doi.org/10.1007/BF02280786

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