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Numerical stability of a quadratic method for solving systems of non linear equations

Numerische Stabilität einer quadratisch konvergenten Methode zur Lösung von Systemen nicht-linearer Gleichungen

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Abstract

In this paper the numerical stability of a recent method to solve systems of nonlinear equations is studied. This method, based on the ε-algorithm, has a quadratic convergence without calculating any derivatives and under quite benevolent conditions. The numerical stability of this algorithm is studied using the theory of theA-stability for the propagation of round-off errors in the numerical integration of differential equations.

Zusammenfassung

In diesem Artikel wird die numerische Stabilität einer neuen Methode zur Lösung von Systemen nicht-linearer Gleichungen studiert. Diese Methode, sie basiert auf dem ε-Algorithmus, ist unter schwachen Voraussetzungen und ohne Verwendung von Ableitungen quadratisch konvergent. Die Stabilität dieses Algorithmus wird unter Verwendung der Theorie derA-Stabilität bezüglich der Fortpflanzung von Rundungsfehlern bei der numerischen Integration von Differentiagleichungen studiert.

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References

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Authors and Affiliations

  1. Lille

    C. Brezinski

  2. Informatique, U. E. R. d' I. E. E. A., BP 36, 59650, Villeneuve d' Ascq, France

    C. Brezinski

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  1. C. Brezinski
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Brezinski, C. Numerical stability of a quadratic method for solving systems of non linear equations. Computing 14, 205–211 (1975). https://doi.org/10.1007/BF02246426

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  • DOI: https://doi.org/10.1007/BF02246426

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