Abstract
We study the convergence of a method of Steffensen-type, which is obtained from the Lagrange polynomial of inverse interpolation with controlled nodes. Conditions are given such that the sequences bilaterally approximate the solution of an equation.
Author
Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)
Keywords
nonlinear equations in R; Steffensen type method; monotone iterations.
Cite this paper as:
I. Păvăloiu, Bilateral approximations of solutions of equations by order three Steffensen-type methods, Studia Univ. Babeş-Bolyai, Mathematica, vol. 51 (2006) no. 3, pp. 105-114.
About this paper
Publisher Name
Babes-Bolyai University
Article on the journal website
Print ISSN
0252-1938
Online ISSN
2065-961x
References
[1] Costabile, F., Gualtieri, I.M., Luceri, R., A new iterative method for the computation of the solution of nonlinear equations, Numer. Algorithms, 28, pp. 87-100, 2001.
[2] Frontini, M., Hermite interpolation and a new iterative method for the computation of the roots of non-linear equations, Calcolo 40, pp. 109-119, 2003.
[3] Grau, M., An improvement to the computing of nonlinear equation solutions, Numer. Algorithms. 34, pp.1-12, 2003.
[4] Ostrowski, A., Solution of Equations in Euclidian and Banach Spaces, Academic Press New York and London, 1973.
[5] Pavaloiu, I., Optimal efficiency index for iterative methods of interpolatory type, Computer Science Journal of Moldova 1, 5, pp. 20-43,1997. 113
[6] Pavaloiu, I., Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo 32, 1-2, pp.69-82, 1995.
[7] Pavaloiu, I., Optimal problems concerning interpolation methods of solution of equations, Publications de L’Institut Mathematique 52 (66) pp 113-126, 1992.
[8] Pavaloiu, I., Optimal effiency index of a class of Hermite iterative methods, with two steps, Rev. Anal. Numer. Theor. Approx. 29, 1, pp. 83-89, 2000.
[9] Pavaloiu, I., Local convergence of general Steffensen type methods, Rev. Anal. Numer. Theor. Approx. 33,1, 79-86, 2004.
[10] Pavaloiu, I., Pop, N., Interpolation and Applications, Risoprint, Cluj-Napoca, 2005 (in Romanian).
[11] Traub, J.F., Iterative Methods for Solutions of Equations, Pretence-Hall Inc., Englewood Cliffs, New Jersey, 1964.
[12] Turowicz, B.A., Sur les derivees d’ordre superieur d’une function inverse, Ann. Polon. Math. 8 pp. 265-269, 1960.