# Numerical Analysis

## 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 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).…

## Observations concerning some approximation methods for the solutions of operator equations

Abstract (soon) AuthorsIon Păvăloiu KeywordsPDFScanned paper. PDF-LaTeX version of the paper. Cite this paper as:I. Păvăloiu, Observations concerning some approximation methods…

## Solving the equations by interpolation

About this bookSummary of the book… (to be completed) CoverAuthorIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis TitleOriginal title (in…

## 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…

## A note on inexact secant methods

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

## 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…