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On the R-order of coupled sequences II

Über die R-Ordnung gekoppelter Folgen II

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Abstract

As in the preceding paper [3], the question whether some of the sequences {x n, i } coupled by a system (3) of inequalities converge at least with a certain R-order τ is reduced to the nonnegative solvability of the system (4) of linear inequalities. Further, the optimal R-order τ implied by (3) is characterized as the spectral radius of a certain matrix composed of exponents appearing in (3).

Zusammenfassung

Die Bestimmung der R-Ordnung τ von Folgen {x n, i ∼, die über ein System (3) von Ungleichungen miteinander verkoppelt sind, wird wie in der vorangegangenen Arbeit [3] auf die nichtnegative Lösbarkeit des Systems (4) von linearen Ungleichungen zurückgeführt. Weiterhin wird gezeigt, daß die beste R-Ordnung τ, welche sich aus (3) herleiten läßt, gleich dem Spektralradius einer bestimmten Matrix ist, welche aus in (3) auftretenden Exponenten gebildet wird.

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References

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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).

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Burmeister, W., Schmidt, J.W. On the R-order of coupled sequences II. Computing 29, 73–81 (1982). https://doi.org/10.1007/BF02254852

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  • DOI: https://doi.org/10.1007/BF02254852

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