A variant of the Newton method

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
(Tiberiu Popoviciu Institute of Numerical Analysis)

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

PDF

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).

About this paper

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

References

?

1978

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