Local convergence of some Newton-type methods for nonlinear systems
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,...,...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2004-08-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/778 |