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.…
(original)
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…
Local convergence of general Steffensen type methods
Abstract We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence…
On the convergence order of some Aitken-Steffensen type methods
Abstract In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods.…