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A class of componentwise Krawczyk-Moore type iteration methods

Ein komponentenweises Iterationsverfahren vom Krawczyk-Moore-Typ

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Abstract

An optimal componentwise Krawczyk-Moore type iteration method is constructed by use of the new centered form of Baumann.

Zusammenfassung

Ein optimales komponentenweises Iterationsverfahren vom Krawczyk-Moore-Typ wird eingeführt. Es benutzt die neue zentrische Form von Baumann.

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References

  1. Baumann, E.: Optimal centered forms. Freiburger Intervall-Berichte 7/3.

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

    Google Scholar 

  3. Hansen, E., Sengupta, S.: Bounding solutions of systems of equations using interval analysis. BIT21, 203–211 (1981).

    Google Scholar 

  4. Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing4, 187–201 (1969).

    Google Scholar 

  5. Krawczyk, R.: Conditionally isotone interval operators. Freiburger Intervall-Berichte, 84/5.

  6. Krawczyk, R., Neumaier, A.: An improved interval Newton operator. J.of Mathematical analysis and applications118, 194–201 (1986).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. Moore, R. E., Qi, L.: A successive interval test for nonlinear systems. SIAM J. Numer. Anal.19, 845–850 (1982).

    Google Scholar 

  10. Neumaier, A.: Existence of solution of piecewise differentiable systems of equations. Arch. Math.47, 443–447 (1986).

    Google Scholar 

  11. Nickel, K.: A globally convergent ball Newton method. SIAM J. Numer. Anal.18, 998–1003 (1981).

    Google Scholar 

  12. Pandian, M. A.: A convergence test and componentwise error estimate for Newton type methods. SIAM J. Numer. Anal.22, 779–791 (1985).

    Google Scholar 

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

  14. Qi, L.: A note on the Moore test for nonlinear systems. SIAM J. Numer. Anal.19, 851–857 (1982).

    Google Scholar 

  15. Wolfe, M. A.: A modification of Krawczyk's algorithm. SIAM J. Numer. Anal.17, 370–379 (1980).

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität Freiburg, Hermann-Herder-Strasse 10, D-7800, Freiburg i. Br., Federal Republic of Germany

    Shen Zuhe

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  1. Shen Zuhe
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Additional information

This paper has been written while the author worked as a visiting professor at the Institut für Angewandte Mathematik of the University of Freiburg i. Br./Federal Republic of Germany. It has been sponsored by the Stiftung Volkswagenwerk, number I/63 064.

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Shen Zuhe A class of componentwise Krawczyk-Moore type iteration methods. Computing 41, 149–152 (1989). https://doi.org/10.1007/BF02238738

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  • DOI: https://doi.org/10.1007/BF02238738

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