It is well known that the Newton and the Chebyshev methods for nonlinear systems require solving of a linear system at each iteration step. In this note we shall study two modified methods whichâ€¦ (More)

We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes controlled by the Newton method. We obtain a local convergence result which showsâ€¦ (More)

In this paper we study the convergence of a Newtonâ€“Steffensen type method for solving nonlinear equations in R, introduced by Sharma [J.R. Sharma, A composite third order Newtonâ€“Steffensen method forâ€¦ (More)

We introduce an Aitkenâ€“Newton iterative method for nonlinear equations, which is obtained by using the Hermite inverse interpolation polynomial of degree 2, with two nodes given by the Newton method.â€¦ (More)

We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show how the auxiliary functions may be constructed and we analyze someâ€¦ (More)