## On the approximation of solutions to nonlinear operators between metric spaces

Abstract A Gauss-Seidel method for linear systems, based on decomposing the matrix system into four submatrices blocks, has been proposed…

## A Halley-Aitken-type method for approximating the solutions of scalar equations

Abstract We are concerned with the approximation of the solution of scalar equations by Halley-Aitken method. We obtain local convergence…

## On the convergence order of the multistep methods

Abstract We analyze in a unitary way the iterative methods for solving scalar equations, which are of inverse interpolation form.…

## On the Chebyshev method for approximating the solutions of polynomial operator equations of degree 2

Abstract The Chebyshev method for approximating the solutions of polynomial operator equations of degree 2 is presented. The convergence of the Chebyshev…

## Optimal efficiency indexes for iterative methods of interpolatory type

Abstract The paper is concerned with the order of convergence and the efficiency index of iterative methods of interpolatory type…

## 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 Steffensen-Hermite type method for approximating the solutions of nonlinear equations

Abstract It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled…

## Accelerating the convergence of the iterative methods of interpolatory type

Abstract In this paper we deal with iterative methods of interpolatory type, for solving nonlinear equations in Banach spaces. We…

## Local convergence of some Newton type methods for nonlinear systems

Abstract In order to approximate the solutions of nonlinear systems $F(x)=0,$ with $$F:D\subseteq {\mathbb R}^n \rightarrow {\mathbb R}^n$$, \(n\in {\mathbb…