Local convergence of some Newton-type methods for nonlinear systems

Journal of Numerical Analysis and Approximation Theory

Ion Păvăloiu¹ 

[1] Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy;

关键词: nonlinear systems of equations;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown