## 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…

Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…

Abstract We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange…

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…

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

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

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…

Abstract We study the approximation of an eigenpair (an eigenvalue and a corresponding eigenvector) of a a linear operator T from…

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…

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 \(X\)…

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…