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