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…
Numerical Analysis
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 (Tiberiu Popoviciu Institute of Numerical Analysis) KeywordsPDFScanned paper. PDF-LaTeX version of the paper. Cite this paper…
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 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 (Tiberiu Popoviciu Institute of Numerical Analysis) Keywords? PDFScanned paper. PDF-LaTeX version of the paper. Cite this paper…
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 \(X\)…