On a robust Aitken-Newton method based on the Hermite polynomial

Abstract We introduce an Aitken–Newton iterative method for nonlinear equations, which is obtained by using the Hermite inverse interpolation polynomial…

Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three

Abstract We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable…

A unified treatment of the modified Newton and chord methods

Abstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…

On a Steffensen-Hermite method of order three

Abstract In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the…

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…

Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences

Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…

Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three

Abstract We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange…

On a third order iterative method for solving polynomial operator equations

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…

On approximating the eigenvalues and eigenvectors of linear continuous operators

Abstract We consider the computing of an eigenpair (an eigenvector $$v=(v^{(i)})_{i=1,n}$$ and an eigenvalue $$\lambda$$) of a matrix $$A\in\mathbb{R}^{n\times n}$$, by…

On the Chebyshev method for approximating the eigenvalues of linear operators

Abstract We study the approximation of an eigenpair (an eigenvalue and a corresponding eigenvector) of a a linear operator T from…