Local convergence of some Newton-type methods for nonlinear systems

Authors

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

Keywords:

nonlinear systems of equations

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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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. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no2-art12

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Section

Articles