## Abstract

## Authors

Ioannis K. **Argyros**

(Cameron University, USA)

Emil **Cătinaş**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Ion **Păvăloiu**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

chord/secant method; semilocal convergence; r-convergence order.

##### Cite this paper as:

I. Argyros, E. Cătinaş, I. Păvăloiu, *Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term*, Rev. Anal. Numér. Théor. Approx., **27** (1998) no. 2, pp. 191-202.

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## About this paper

##### Publisher Name

##### Paper on the journal website

##### Print ISSN

1222-9024

##### Online ISSN

2457-8126

##### MR

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## References

[1] K. Argyros, *On the solution of equations with nondifferentiable operators and the Ptak error estimates*, BIT, 30 (1990), pp. 752-754.

[2] I. K. Argyros, *On the solution of nonlinear equations with a nondifferentiable term*, Rev. Anal. Numer. Theor. Approx., 22 (1993) 2, pp. 125-135.

[3] I. K. Argyros, *On some iterative methods for solving nonlinear equations with a nondifferentiable term of order between 1.618… and 1.839*. (submitted to this joumal).

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[5] E. Cătinaș, *On some iterative methods for solving nonlinear equations*, Rev. Anal. Numer. Theor. Approx., 23, I (1994), pp. 47-53.

[6] G. Goldner, and M. Balazs, *Remarks on divided differences and method of chords*, Rev. Anal. Numer. Theor. Approx., 3, I (1974), pp. 19-30.

[7] L. V. Kantorovich, *The method of successive approximation for functional equation*s, Acta Math. 71 (1939), pp. 63-97.

[8] J. M. Ortega and W. C. Rheinboldt, *Iterative Solution of Nonlinear Equations in Several Variables*, Academic Press, New York, 1970.

[9] I. Păvăloiu, *Sur une generalisation de la methode de Steffensen*, Rev. Anal. Numer. Theor. Approx., 21, 1 (1992), pp. 59-65.

[10] I. Păvăloiu, *A convergence theorem concerning the chord methods,* Rev. Anal. Numer. Theor. Approx., 22, 1 (1993), pp. 83-85.

[11] F. A, Potra, *On an iterative algorithm of order 1.839 . . . for solving nonlinear equations*, Numer. Funct. Anal. Optimiz. 7, I (1984-1985), pp. 75-106.

[12] T. Yamamoto and X. Chen, *Convergence domains of certain iterative methods for solving nonlinear equations*, Numer. Funct. Anal. Optimiz. 10, 1 and 2 (1989), pp.37-48.