Parameter-based algorithms for approximating local solution of nonlinear complex equations


  • Ioannis K. Argyros Cameron University, Oklahoma.
  • Dong Chen University of Arkansas, Arkansas.



Nonlinear equations, Halley- Werner type methods, Ostrowski-Kantorovich analysis, Upper error bound


We study the Ostrowski-Kantorovich convergence for a family of Halley- Werner type iteration methods in the complex plane. We provide an upper error bound for all parameter ? ? [1 , 2). We show that the error bound is a decreasing function of ?. We prove also that the Halley method has the largest error bound.

Author Biographies

Ioannis K. Argyros, Cameron University, Oklahoma.

 Department of Mathematics.


Dong Chen, University of Arkansas, Arkansas.

Department of Mathematical Sciences.


[1] E. Halley, A New Exact and Easy Method of Finding the Roots of equations Generally and that Without any Previous Reduction, Phil. Trans. Roy. London, 18(1694), 134-145.

[2] W. B. Gragg and R.A. Tapia, Optimal Error Bounds for the Newton-Kantorovich Theorem, SIAM J. Numer.Anal., 11(1974), 10-13.

[3] L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1977.

[4] A.M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, Third Edition, New York, 1973.

[5] W. Werner, Some Improvements of Classical Iterative Methods for the Solutions of Nonlinear Equations, Lecture Notes in Mathematics, Numerical Solution of Nonlinear Equations, Proceedings, Bremen, 878( 1980), 427-440.



How to Cite

I. K. Argyros and D. Chen, “Parameter-based algorithms for approximating local solution of nonlinear complex equations”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 53-61, Apr. 2018.




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