## Abstract

Let \(X\) be a Banach space, \(Y\) a normed space, \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left( x\right) =0\). The first order derivative is approximated by the partial derivative of an operator of two variables, whose diagonal restrictive coincides with \(P\). We give a semilocal convergence result for the considered method.

## Authors

Ion Păvăloiu

## Title

### Original title (in French)

*Une variante de la méthode de Newton*

### English translation of the title

*A variant of the Newton method*

## Keywords

two step Newton type method; semilocal convergence; nonlinear equation in Banach space

## References

## About this paper

##### Cite this paper as:

I. Păvăloiu, *Une variante de la méthode de Newton*, Anal. Numér. Théor. Approx., **7** (1978) no. 1, pp. 95-99 (in French).

##### Journal

Mathematica – Revue d’Analyse Numérique et de Théorie de l’Approximation

L’Analyse Numérique et la Théorie de l’Approximation

##### Publisher Name

Editura Academiei R.S. Romane.

##### Article on journal website

##### Print ISBN

1010-3376

##### Online ISBN

2457-8118