Skip to main content
SpringerLink
Log in

On the convergence of a class of newton-like methods

  • Monotone Iterations And Computational Error Bounds
  • Conference paper
  • First Online:
Iterative Solution of Nonlinear Systems of Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 953))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ALEFELD, G.: Monotone Regula-Falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen, Beiträge zur Numerische Mathematik, 8(1979).

    Google Scholar 

  2. BOSARGE, W.E. and FALB, P.L.: A multipoint method of third order, J.Optimiz.Theory Appl., 4(1969), 156–166.

    Article  MathSciNet  MATH  Google Scholar 

  3. BOSARGE, W.E.; and FALB, P.L.: Infinit dimensional multipoint methods and the solution of two point boundary value problems, Numer.Math., 14(1970), 264–286.

    Article  MathSciNet  MATH  Google Scholar 

  4. DENNIS, J.E.: On the Kantorovich hypothesis for Newton's method, SIAM J.Numer.Anal., 6, 3(1969), 493–507.

    Article  MathSciNet  MATH  Google Scholar 

  5. DENNIS, J.E.: Toward a unified convergence theory for Newton-like methods, in Nonlinear Functional Analysis and Applications, L.B. Rall, Ed., Academic Press, New York, 1971.

    Google Scholar 

  6. DEUFLHARD, P. and HEINDL, G.: Affine invariant convergence theorems for Newton's method and extensions to related methods, SIAM J.Numer.Anal., 16(1979), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  7. GRAGG, W.B. and TAPIA, R.A.: Optimal error bounds for the Newton-Kantorowich theorem, SIAM J.Numer.Anal., 11(1974), 10–13.

    Article  MathSciNet  MATH  Google Scholar 

  8. KANTOROVICH, L.V.: The method of successive approximations for functional equations, Acta Math., 71(1939), 63–97.

    Article  MathSciNet  Google Scholar 

  9. LAASONEN, P.: Ein überquadratisch konvergenter iterativer Algorithmus. Ann.Acad.Sci.Fenn.Ser.A. I, 450(1969), 1–10.

    MATH  Google Scholar 

  10. MIEL, G.J.: An updated version of the Kantorovich theorem for Newton's method. Technical Summary Report, Mathematical Research Center, University of Wisconsin Madison, 1980.

    Google Scholar 

  11. ORTEGA, J.M. and RHEINBOLDT, W.C.: Monotone iteration for nonlinear equations with application to Gauss-Sudel methods, SIAM J.Numer.Anal., 4(1967), 171–190.

    Article  MathSciNet  MATH  Google Scholar 

  12. POTRA, F.-A.: On the aposteriori error estimates for Newton's method, Preprint Series in Mathematics, INCREST, Bucharest, no. 19/1981.

    MATH  Google Scholar 

  13. POTRA, F.-A.: A general iterative procedure for solving nonlinear equations in Banach spaces, Preprint Series in Mathematics, INCREST, Bucharest, no.37/1981.

    Google Scholar 

  14. POTRA, F.-A. and PTÁK, V.: Sharp error bounds for Newton's method, Numer.Math., 34(1980), 63–72.

    Article  MathSciNet  MATH  Google Scholar 

  15. POTRA, F.-A. and PTÁK, V.: On a class of modified Newton processes, Numer.Func-Anal. and Optimiz., 2, 1(1980), 107–120.

    Article  MathSciNet  MATH  Google Scholar 

  16. POTRA, F.-A. and PTÁK, V.: A generalization of Regula Falsi Numer.Math., 36(1981), 333–346.

    Article  MathSciNet  MATH  Google Scholar 

  17. POTRA, F.-A. and SCHMIDT, J.W.: On a class of iterative procedures with monotonous convergence, Preprint Series in Mathematics, INCREST, Bucharest, no.3/1982.

    Google Scholar 

  18. SCHMIDT, J.W.: Eine Übertragung der Regula Falsi auf Gleichungen in Banachraum, I, II, Z.Angew.Math.Mech., 43(1963), 1–8, 97–110.

    Article  MathSciNet  MATH  Google Scholar 

  19. SCHMIDT, J.W. and LEONHARDT, H.: Eingrenzung von Lösungen mit Hilfe der Regula Falsi, Computing, 6(1970), 318–329.

    Article  MathSciNet  MATH  Google Scholar 

  20. SCHMIDT, J.W. and SCHWETLICK, H.: Ableitungsfreie Verfahren mit höherer Konvergenzgeschwindigkeit, Computing, 3(1968), 215–226.

    Article  MathSciNet  MATH  Google Scholar 

  21. SCHNEIDER, N.: Monotone Einschliessung durch Verfahren von Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungs-beriffes, Computing, 26(1981), 33–44.

    Article  MathSciNet  MATH  Google Scholar 

  22. TRAUB, J.F.: Iterative methods for the solution of equations, Prentice Hall, Englewood Cliffs, New Jersey, 1964.

    MATH  Google Scholar 

  23. VANDERGRAFT, J.S.: Newton's method for convex operators in partially ordered spaces, SIAM J.Numer.Anal., 4(1967), 406–432.

    Article  MathSciNet  MATH  Google Scholar 

  24. WOLFE, M.A.: Extended iterative methods for the solution of operator equations, Numer.Math., 31(1978), 153–174.

    Article  MathSciNet  MATH  Google Scholar 

  25. WOLFE, M.A.: On the convergence of some methods for determining zeros of order-convex operators, Computing, 26(1981), 45–56.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The National Institute for Scientific and Technical Creation, Bd.Pacii 220, 79622, Bucharest, Romania

    F.-A. Potra

Authors
  1. F.-A. Potra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rainer Ansorge Theodor Meis Willi Törnig

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Potra, FA. (1982). On the convergence of a class of newton-like methods. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069378

Download citation

  • DOI: https://doi.org/10.1007/BFb0069378

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation