## On the Steffensen method for solving nonlinear operator equations

Abstract We consider the equation $F\left( x\right) =x-A\left( x\right)=0,$ where $$A$$ is an operator from a Banach space $$X$$ to…

## 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 monotonicity of the sequences of approximations obtained by Steffensen’s method

Abstract   AuthorIon Păvăloiu KeywordsReferences[1] Balazs, M., A bilateral approximating method for finding the real roots of real equations. Rev. Anal.…

## 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…

## A note on inexact secant methods

Abstract The inexact secant method $$[x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k$$, $$x_{k+1}=x_k+s_k$$, $$k=1,2,\ldots$$, $$x_0,x_1 \in {\mathbb R}^n$$ for solving the nonlinear system…

## On some Steffensen-type iterative methods for a class of nonlinear equations

Abstract Consider the nonlinear equations $$H(x):=F(x)+G(x)=0$$, with $$F$$ differentiable and $$G$$ continuous, where $$F,G,H:X \rightarrow X$$ are nonlinear operators and $$X$$…

## On some iterative methods for solving nonlinear equations

Abstract Consider the nonlinear equation $$H(x):=F(x)+G(x)=0$$, with $$F$$ differentiable and $$G$$ continuous, where $$F,G,H:X \rightarrow X$$, $$X$$ a Banach space.  The…

## 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…