Error estimation in numerical solution of equations and systems of equations
Abstract In \cite{7 Urabe}, \cite{8 Urabe} M. Urabe studies the numerical convergence and error estimation in the case of operatorial equation…
Optimal problems concerning interpolation methods of solution of equations
Abstract We consider optimality problems regarding the order of convergence of the iterative methods which are obtained by inverse interpolation…
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.…