# semilocal convergence

## Sufficient convergence conditions for certain accelerated successive approximations

Abstract We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

## 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 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 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…

## 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 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…

## 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…

## On the iterative methods with high convergence orders

Abstract Let $$X$$ be a Banach space and $$Y$$ a normed space, and $$P:X\rightarrow Y$$ a nonlinear operator. In order…