## On some interpolation iterative methods with optimal convergence speed

Abstract We consider nonlinear equations in $$\mathbb{R}$$, and a class of iterative methods obtained by inverse interpolation of Hermite type.…

## On the efficiency of the computations for approximating the solutions of equations

Abstract We consider the iterative methods for solving nonlinear equations in $$\mathbb{R}$$ and the class of iterative methods obtained by…

## On some interpolatory iterative methods for the second degree polynomial operators (I)

Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…

## On an approximation formula

Abstract We generalize an approximation formula which in some particular cases has been studied by [J.F. Traub 1964] and \…

## On some interpolatory iterative methods for the second degree polynomial operators (II)

Abstract In this paper we apply some iterative methods obtained by inverse interpolation, in order to solve some specific classes…

## Monotone sequences for approximating the solutions of equations

Abstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…

## On the convergence order of the iterative methods

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…

## Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices

Abstract We consider a square matrix $$A$$ with real or complex elements. We denote $$\mathbb{K}=\mathbb{R}$$ or $$\mathbb{C}$$ and we are…

## Optimal algorithms concerning the solving of equations by interpolation

Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…

## On a generalization of the Steffensen method

Abstract We extend the Steffensen method for solving the equation $$f\left( x\right)=0$$ to the setting of the Banach spaces, \(f:X\rightarrow…