Local convergence of some Newton-type methods for nonlinear systems

Ion Păvăloiu

doi:10.33993/jnaat332-778

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: 266

Abstract

In order to approximate the solutions of nonlinear systems

F (x) = 0,

with

F : D \subseteq R^{n} \to R^{n}

,

n \in N

, we consider the method

\begin{aligned} x_{k + 1} & = x_{k} - A_{k} F (x_{k}) \\ A_{k + 1} & = A_{k} (2 I - F^{'} (x_{k + 1}) A_{k}), k = 0, 1, . . ., A_{0} \in M_{n} (R), x_{0} \in D, \end{aligned}

and we study its local convergence.

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References

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