Computing

, Volume 38, Issue 1, pp 75–87 | Cite as

Some modifications of the parallel Halley iteration method and their convergence

  • De-ren Wang
  • Yu-jiang Wu
Short Communications

Abstract

In this paper we derive five kinds of algorithms for simultaneously finding the zeros of a complex polynomial. The convergence and the convergence rate with higher order are obtained. The algorithms are numerically illustrated by an example of degree 10, and the numerical results are satisfactory.

AMS Subject Classification

65H05 

Key words

Complex polynomial zeros parallel Halley iteration method convergence order 

Einige Varianten des parallelen Halleyschen Iteractionsverfahrens und ihre Konvergenz

Zusammenfassung

In dieser Arbeit leiten wir fünf Varianten eines Algorithmus zur parallelen Bestimmung der Nullstellen eines komplexen Polynoms her. Ihre Konvergenz und deren Rate höherer Ordung werden bestimmt. Die Algorithmen werden an einem Beispiel vom Grad 10 numerisch illustriert, die Ergebnisse sind zufriedenstellend.

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References

  1. [1]
    Alefeld, G., Herzberger, J.: On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots. SIAM J. Numer. Anal.11, 237–243 (1974).CrossRefGoogle Scholar
  2. [2]
    Gargentini, I., Henrici, P.: Circular arithmetic and the determination of polynomial zeros. Numer. Math.18, 305–320 (1972).CrossRefGoogle Scholar
  3. [3]
    Milovanović, G. V., Petković, M. S.: On the convergence order of a modified method for simultaneous finding polynomial zeros. Computing30, 171–178 (1983).Google Scholar
  4. [4]
    Wang, Xing-hua, Zheng, Shi-ming: Parallel Halley iteration method with circular arithmetic for finding all zeros of a polynomial. A Journal of Chinese University, Numer. Math.4, 308–314 (1985).Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • De-ren Wang
    • 1
  • Yu-jiang Wu
    • 2
  1. 1.Department of MathematicsShanghai University of Science and TechnologyShanghaiThe People's Republic of China
  2. 2.Department of Mathematics and MechanicsLanzhou UniversityLanzhou, GansuThe People's Republic of China

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