Computing

, Volume 47, Issue 3–4, pp 355–360 | Cite as

On the generalization of the Alefeld-Herzberger's method

  • N. Kjurkchiev
  • A. Andreev
Article

Abstract

In this note we consider a class of iteration methods which is a generalization of those in [2], for the determination of simple roots of an algebraic equation. Estimates for theirR-order are derived.

AMS Subject Classifications

65H05 65G10 

Key words

Iterative methods polynomial equations P-order of convergence spectral radius multiple zeros 

Zur Verallgemeinerung von Alefeld-Herzberger-Verfahren

Zusammenfassung

Wird betrachten in dieser Arbeit eine Klasse von Iterationsverfahren, die eine Verallgemeinerung von den in [2] behandelten ist, zur Einschließung einfacher Wurzeln einer algebraischen Gleichung. Dazu werden Abschätzungen für dieR-Ordnung hergeleitet.

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References

  1. [1]
    Ehrlich, L.: A modified Newton method for polynomials. Communs. ACM10, 107–108 (1967).MATHGoogle Scholar
  2. [2]
    Alefeld, G., Herzberger, J.: On the convergence speed of some algorithms for the simultaneous approximation of polynomial. SIAM, J. Numer. Anal.11, 237–243 (1974).CrossRefMathSciNetGoogle Scholar
  3. [3]
    Ortega, J., Rheinboldt, W.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970.Google Scholar
  4. [4]
    Kjurkchiev, N., Andreev, A.: Ehrlich's method with raised speed of convergence. Serdika13, 52–57 (1987).MathSciNetGoogle Scholar
  5. [5]
    Deutsch, E.: Lower bounds for the Perron root of a nonnegative irreducible matrix. Math. Proc. Camb. Philos. Soc.92, 49–54 (1982).MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • N. Kjurkchiev
    • 1
  • A. Andreev
    • 1
  1. 1.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria

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