Local convergence of some Newton-type methods for nonlinear systems

Authors

  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat332-778

Keywords:

nonlinear systems of equations
Abstract views: 220

Abstract

In order to approximate the solutions of nonlinear systems\[F(x)=0,\]with \(F:D\subseteq {\mathbb R}^{n}\rightarrow {\mathbb R}^{n}\),\(n\in {\Bbb N}\), we consider the method\begin{align*}x_{k+1} & =x_{k}-A_{k}F(x_{k})\label{f1.4}\\A_{k+1} & =A_{k}(2I-F^{\prime}(x_{k+1})A_{k}),\;k=0,1,..., \,A_{0}\in M_{n}({\Bbb R}), x_0 \in D,\end{align*}and we study its local convergence.

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References

Cătinaş, E. and Păvăloiu, I., On approximating the eigenvalues and eigenvectors of linear continuous operators, Rev. Anal. Numér. Théor. Approx., 26, nos. 1-2, pp. 19-27, 1997, http://ictp.acad.ro/jnaat/journal/article/view/1997-vol26-nos1-2-art3

Diaconu, A., On the convergence of an iterative proceeding of Chebyshev type, Rev. Anal. Numér. Théor. Approx., 24, nos. 1-2, pp. 19-27, 1995, http://ictp.acad.ro/jnaat/journal/article/view/1995-vol24-nos1-2-art9

Diaconu, A. and Păvăloiu, I., Sur quelques méthodes itératives pour la résolution des equations opérationelles, Rev. Anal. Numér. Théor. Approx., 1, no. 1, pp. 45-61, 1972, http://ictp.acad.ro/jnaat/journal/article/view/1972-vol1-art3 DOI: https://doi.org/10.33993/jnaat11-3

Lazăr, I., On a Newton type method, Rev. Anal. Numér. Théor. Approx., 23, no. 2, pp. 167-174, 1994, http://ictp.acad.ro/jnaat/journal/article/view/1994-vol23-no2-art5

Păvăloiu, I., Introduction in the Theory of Approximating the Solutions of Equations, Ed. Dacia, Cluj-Napoca, 1976 (in Romanian).

Ulm, S., On the iterative method with simultaneous approximation of the inverse of the operator, Izv. Nauk. Estonskoi S.S.R., 16, no. 4, pp. 403-411, 1967.

Zehnder, J. E., A remark about Newton's method, Comm. Pure Appl. Math., 37, pp. 361-366, 1974 https://doi.org/10.1002/cpa.3160270305. DOI: https://doi.org/10.1002/cpa.3160270305

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Published

2004-08-01

How to Cite

Păvăloiu, I. (2004). Local convergence of some Newton-type methods for nonlinear systems. Rev. Anal. Numér. Théor. Approx., 33(2), 209–213. https://doi.org/10.33993/jnaat332-778

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