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Truncated nonlinear ABS algorithm and its convergence property

Abgeschnittener nichtlinearer ABS-Algorithmus und seine Konvergenzeigenschaften

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Abstract

This paper shows that the nonlinear ABS algorithm [1] can be viewed as inexact Newton method [3]. From this point of view, the truncated nonlinear ABS algorithm is established and its convergence property is discussed.

Zusammenfassung

Diese Arbeit zeigt, daß der nichtlineare ABS-Algorithmus [1] als unexakte Newton-Methode [3] angesehen werden kann. Aus dieser Sicht wird der abgeschnittene nichtlineare ABS-Algorithmus hergeleitet und seine Konvergenzeigenschaft diskutiert.

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References

  1. Abaffy, J., Galantai, A., Spedicato, E., The local convergence of ABS methods for nonlinear algebraic system, Numer. Math.,51 (1987), 429–439.

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  2. Abaffy, J., Spedicato, E., ABS projection algorithms, Mathematical techniques for linear and nonlinear equations, John Wiley & Sons, 1989.

  3. Dembo, R. S., Eisenstat, S. C., Steihaug, T., Inexact Newton methods. SIAM J. Numer. Anal.,19 (1982), 400–408.

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  4. Zhu, M., A generalization of nonlinear ABS algorithms and its convergence Journal of Beijing Polytechnic University,15, (1989), No 4, 21–26.

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Deng, N., Chen, Z. Truncated nonlinear ABS algorithm and its convergence property. Computing 45, 169–173 (1990). https://doi.org/10.1007/BF02247882

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  • DOI: https://doi.org/10.1007/BF02247882

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