On the secant method and the Ptak error estimates

Authors

  • Ioannis K. Argyros Cameron Universtity, Lawton, United States

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References

Argyros, I.K., On Newton's method and nondiscrete mathematical induction, Bull. Austral. Math. Soc. 38, (1988), pp. 131-140.

Argyros, I.K., The Secant method and fixed points of nonlinear operators, Mh. Math. 106, (1988), pp. 85-94.

Balasz, M. and Goldner, G., On the method of the cord and on a modification of it for the solution of nonlinear operators equations. Stud. Cerc. Mat. 20, (1968), pp. 981-990.

Potra, F.S., Sharp error bounds for a class of Newton-like methods, Libertas Mathematica, Bol. 5, (1985), pp. 72-84.

Potra, F.A., and Pták, V., Sharp error bounds for Newton's process. Numer. Math. 34, (1980), pp. 63-72, https://doi.org/10.1007/BF01463998.

Potra, F.A., and Pták, V., Nondiscrete induction and iterative processes. Boston: Pitman, 1984.

Yamamoto, T., a method for finding sharp error bounds for Newton's method under the Kantorovich assumptions, Numer. Math. 44, (1986), pp. 203-220, https://doi.org/10.1007/BF01389624.

Zabrejko, P.P. and Nguen, D.F., The majorant method in the theory of Newton-Kantorovich assumptions. Numer. Math. 44, (1986), pp. 203-220, https://doi.org/10.1080/01630568708816254

Zincenko, A.I., Some approximate methods of solving equations with nondifferentiable operators. (Ukrainian). Dopovidi Akad. Nauk. Ukrain. RSR (1963), pp. 156-161.

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Published

1995-08-01

How to Cite

Argyros, I. K. (1995). On the secant method and the Ptak error estimates. Rev. Anal. Numér. Théor. Approx., 24(1), 3–14. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1995-vol24-nos1-2-art1

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