Region of accessibility for a class of Newton-type iterations
DOI:
https://doi.org/10.22199/S07160917.1998.0001.00006Keywords:
Nonlinear equations in the cornplex plane, Second-order processes, Newton's method, The contraction mapping principleAbstract
We consider in this paper, for a family of Newton-type iterative processes, the questions of existence, uniqueness, and construction of approximations of fixed points of complex functions which satisfy certain simple conditions, as well as the problem of error estimation for approximate solutions.
References
[1] EZQUERRO, J.A. AND HERNÁNDEZ, M.A., A Note on a Farnily of Newton Type Iterative Processes. Intern. J. Computer Math. 62, pp. 223-232, (1996).
[2] GUTIÉRREZ, J.M., HERNÁNDEZ, M.A. AND SALANOVA, M.A., Accessibility of Solutions by Newton's Method. Intern. J. Computer Math. 57, pp. 239-247, (1995).
[3] HERNÁNDEZ, M.A., A Note on Halley's Method. Numer. Math. 59, 3, pp. 273-276, (1991).
[4] HERNÁNDEZ, M.A., Newton-Raphson's Method and Convexity, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 22, 1, pp. 159-166, (1992).
[5] HERNÁNDEZ, M.A. AND SALANOVA, M.A., A Farnily of Newton Type Iterative Processes. Intern. J. Computer Math. 51, pp. 205-214, (1994).
[6] RALL, L.B., Computational Solution ofNonlinear Operator Equations. Robert E. Krieger Publishing Company, Inc., (1979).
[2] GUTIÉRREZ, J.M., HERNÁNDEZ, M.A. AND SALANOVA, M.A., Accessibility of Solutions by Newton's Method. Intern. J. Computer Math. 57, pp. 239-247, (1995).
[3] HERNÁNDEZ, M.A., A Note on Halley's Method. Numer. Math. 59, 3, pp. 273-276, (1991).
[4] HERNÁNDEZ, M.A., Newton-Raphson's Method and Convexity, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 22, 1, pp. 159-166, (1992).
[5] HERNÁNDEZ, M.A. AND SALANOVA, M.A., A Farnily of Newton Type Iterative Processes. Intern. J. Computer Math. 51, pp. 205-214, (1994).
[6] RALL, L.B., Computational Solution ofNonlinear Operator Equations. Robert E. Krieger Publishing Company, Inc., (1979).
Published
2018-04-04
How to Cite
[1]
J. A. Ezquerro and M. A. Hernández, “Region of accessibility for a class of Newton-type iterations”, Proyecciones (Antofagasta, On line), vol. 17, no. 1, pp. 71-76, Apr. 2018.
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