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Interval operators and fixed intervals

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Interval Mathematics 1985 (IMath 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 212))

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References

  1. Adams, E.: On Sets of Solutions of Collections of Nonlinear Systems in \(\mathbb{I}\mathbb{R}^n\). Interval Mathematics 1980, ed. by K. Nickel. Academic Press, New York-London-Toronto, 247–256 (1980).

    Google Scholar 

  2. Alefeld, G.: Über die Durchführbarkeit des Gauss'schen Algorithmus bei Gleichungen mit Intervallen als Koeffizienten. Computing Suppl. 1, 15–19 (1977).

    Google Scholar 

  3. Alefeld, G.: On the Convergence of some Interval-Arithmetic Modifications of Newton's Method. SIAM J. Num. Anal. 21, 363–372 (1984).

    Article  Google Scholar 

  4. Alefeld, G. and Herzberger, J.: Über das Newton-Verfahren bei nichtlinearen Gleichungssystemen. ZAMM 50, 773–774 (1970).

    Google Scholar 

  5. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations. Academic Press, New York, 1983.

    Google Scholar 

  6. Alefeld, G. and Platzöder, L.: A Quadratically Convergent Krawczyk-like Algorithm. SIAM J. Num. Anal. 20, 210–219 (1983).

    Article  Google Scholar 

  7. Garloff, J. and Krawczyk, R.: Optimal Inclusion of a Solution Set. Freiburger Intervall-Berichte 84/8, 13–33 (1984).

    Google Scholar 

  8. Gay, D. M.: Pertubation Bounds for Nonlinear Equations. SIAM J. Num. Anal. 18, 654–663 (1981).

    Article  Google Scholar 

  9. Gay, D. M.: Computing Pertubation Bounds for Nonlinear Algebraic Equations. SIAM J. Num. Anal. 20, 638–651 (1983).

    Article  Google Scholar 

  10. Hansen, E.: Interval Forms of Newtons Method. Comp. 20, 153–163 (1978).

    Google Scholar 

  11. Hansen, E. and Smith, R.: Interval Arithmetic in Matrix Computations, Part II. SIAM J. Num. Anal. 4, 1–9 (1967).

    Article  Google Scholar 

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

    Google Scholar 

  13. Krawczyk, R.: Intervalliterationsverfahren. Freiburger Intervall-Berichte 83/6 (1983).

    Google Scholar 

  14. Krawczyk, R.: Interval Iteration for Including a Set of Solutions. Comp. 32, 13–31 (1984).

    Google Scholar 

  15. Krawczyk, R.: Properties of Interval Operators. Freiburger Intervall-Berichte 85/3, 1–20 (1985).

    Google Scholar 

  16. Krawczyk, R. and Neumaier, A.: An Improved Interval Newton Operator. Freiburger Intervall-Berichte 84/4, 1–26 (1984).

    Google Scholar 

  17. Krawczyk, R. and Neumaier, A.: Interval Newton Operators for Function Strips. Freiburger Intervall-Berichte 85/7, 1–34 (1985).

    Google Scholar 

  18. Li, Q. Y.: Order Interval Newton Methods for Nonlinear Systems. Freiburger Intervall-Berichte 83/8 (1983).

    Google Scholar 

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

    Google Scholar 

  20. Moore, R. E.: A Test for Existence of Solutions to Nonlinear Systems. SIAM J. Numer. Anal. 14, 611–615 (1977).

    Article  Google Scholar 

  21. Moore, R. E.: New Results on Nonlinear Systems. Interval Mathematics 1980, ed. by K. Nickel, 165–180 (1980).

    Google Scholar 

  22. Neumaier, A.: New Techniques for the Analysis of Linear Interval Equations. Linear Algebra Appl. 58, 273–325 (1984).

    Article  Google Scholar 

  23. Neumaier, A.: An Interval Version of the Secant Method. BIT 24, 366–372 (1984).

    Google Scholar 

  24. Neumaier, A.: Interval Iteration for Zeros of Systems of Equations. BIT 25, 256–273 (1985).

    Google Scholar 

  25. Neumaier, A.: Existence of Solutions of Piecewise Differentiable Systems of Equations. Freiburger Intervall-Berichte 85/4, 27–34 (1985).

    Google Scholar 

  26. Neumaier, A.: Further Results on Linear Interval Equations. Freiburger Intervall-Berichte 85/4, 37–72 (1985).

    Google Scholar 

  27. Nickel, K.: On the Newton Method in Interval Analysis. MRC Technical Summary Report # 1136, University of Wisconsin, Madison (1971).

    Google Scholar 

  28. Nickel, K.: A Globally Convergent Ball Newton Method. Comp. 24, 97–105 (1980).

    Google Scholar 

  29. Qi, L. Q.: A Generalization of the Krawczyk-Moore Algorithm. ‘Interval Mathematics 1980', ed. by K. Nickel. Academic Press, 481–488, (1980).

    Google Scholar 

  30. Reichmann, K.: Abbruch beim Intervall — Gauss-Algorithmus. Comp. 22, 355–361 (1979).

    Google Scholar 

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Authors
  1. R. Krawczyk
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Karl Nickel

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© 1986 Springer-Verlag Berlin Heidelberg

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Krawczyk, R. (1986). Interval operators and fixed intervals. In: Nickel, K. (eds) Interval Mathematics 1985. IMath 1985. Lecture Notes in Computer Science, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16437-5_8

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  • DOI: https://doi.org/10.1007/3-540-16437-5_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16437-1

  • Online ISBN: 978-3-540-39779-3

  • eBook Packages: Springer Book Archive

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