Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term

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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1222-9024

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2457-8126

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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).

[4] I. K. Arglros, and F. Szidarovszky, The Theory and Application of lteration Method, CRC Press, Inc., Boca Raton, Florida, 1993.

[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 equations, 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.

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