On an approximation formula6 years agoAbstract We generalize an approximation formula which in some particular cases has been studied by [J.F. Traub 1964] and \…
On some interpolatory iterative methods for the second degree polynomial operators (II)6 years agoAbstract In this paper we apply some iterative methods obtained by inverse interpolation, in order to solve some specific classes…
Monotone sequences for approximating the solutions of equations6 years agoAbstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…
On the convergence order of the iterative methods6 years agoAbstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…
Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices6 years agoAbstract We consider a square matrix \(A\) with real or complex elements. We denote \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\) and we are…
Optimal algorithms concerning the solving of equations by interpolation6 years agoAbstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…
On a generalization of the Steffensen method6 years agoAbstract We extend the Steffensen method for solving the equation \(f\left( x\right)=0\) to the setting of the Banach spaces, \(f:X\rightarrow…
Remarks on the secant method for the solution of nonlinear operator equations6 years agoAbstract Let \(X_{1},X_{2}\) be two Banach spaces and \(f:X_{1}\rightarrow X_{2}\) a nonlinear equation. We study the chord method for solving…
On the convergency of a Steffensen-type method6 years agoAbstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping. We study the convergence of the Steffensen method for…
On the chord method6 years agoAbstract Let \(X_{1},X_{2}\) be two Banach spaces, \(f:X_{1}\rightarrow X_{2}\) a nonlinear mapping and consider the chord method for solving the…