A variant of the Newton method

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.

Ion Păvăloiu

Original title (in French)

Une variante de la méthode de Newton

English translation of the title

A variant of the Newton method

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

Scanned paper.

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

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