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Interval boxes of solutions of nonlinear systems

Intervall-Einschließungen von Lösungen nichtlinearer Gleichungssysteme

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Abstract

A variation of the Krawczyk operator for including the solutions of a nonlinear system is introduced here. It improves the Krawczyk operatorK (X) wheneverK i (X)⊂int (X i ) for somei. A comparison with other variations is also given.

Zusammenfassung

Es wird eine Modifikation des Krawczyk-OperatorsK(X) zur Einschließung von Lösungen nichtlinearer Gleichungssysteme behandelt. Wenn für mindestens eine Komponentei die EinschließungK i (X)⊂int (X i ) gilt, kann der OperatorK(X) verbessert werden. Außerdem wird das verbesserte Verfahren mit anderen Modifikationen verglichen.

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References

  1. Hansen, E.: Interval forms of Newton's method. Computing20, 153–163 (1980).

    Google Scholar 

  2. Hansen, E., Sengupta, S.: Bounding solutions of systems of equations using interval analysis, to BIT. (Submitted, 1980.)

  3. Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen, mit Fehlerschranken. Computing24, 187–201 (1969).

    Google Scholar 

  4. Krawczyk, R.: Interval extensions and interval iterations. Computing24, 119–129 (1980).

    Google Scholar 

  5. Krawczyk, R.: Zur Konvergenz iterierter Mengen. Freiburger Intervall-Berichte80/3, 1–32 (1980).

    Google Scholar 

  6. Krawczyk, R., Selsmark, F.: Orderconvergence and iterative interval methods. J. Math. Anal. Appl.73 (1980).

  7. Moore, R. E.: Interval Analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966.

    Google Scholar 

  8. Moore, R. E.: A test, for existence of solutions to nonlinear systems. SIAM J. Numer. Anal.14, 611–615 (1977).

    Google Scholar 

  9. Moore, R. E.: A computational test for convergence of iterative methods for nonlinear systems. SIAM J. Numer. Anal.15, 1194–1196 (1978).

    Google Scholar 

  10. Qi, L.: A generalization of the Krawczyk-Moore algorithm. In: Interval Mathematics—Proceedings of 1980 Interval Symposium (Nickel, K., ed.), pp. 481–488. New York: Academic Press 1980.

    Google Scholar 

  11. Rall, L. B.: A comparison of the existence theorems of Kantorovich and Moore. SIAM J. Numer. Anal.17, 148–161 (1980).

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Tsinghua University, Beijing, The People's Republic of China

    L. Qi

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  1. L. Qi
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Qi, L. Interval boxes of solutions of nonlinear systems. Computing 27, 137–144 (1981). https://doi.org/10.1007/BF02243547

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  • DOI: https://doi.org/10.1007/BF02243547

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