On an Aitken-Newton type method

Abstract We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes…

On a Newton-Steffensen type method

Abstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…

On a Steffensen type method

Abstract We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show…

A note on inexact secant methods

Abstract The inexact secant method \([x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k\), \( x_{k+1}=x_k+s_k\), \( k=1,2,\ldots\), \( x_0,x_1 \in {\mathbb R}^n\) for solving the nonlinear system…

On an Aitken type method

Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…

local convergence

assuming a solution exists, one gives conditions such that iterates chosen sufficiently close to that solution converge to that solution.

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