Monotone sequences for approximating the solutions of equations
Abstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…
(original)
On the convergence order of the iterative methods
Abstract 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 matrices
Abstract We consider a square matrix \(A\) with real or complex elements. We denote \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\) and we are…
On a generalization of the Steffensen method
Abstract 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 equations
Abstract 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 method
Abstract 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 method
Abstract 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…
On a Steffensen type method for solving nonlinear operator equations
Abstract Let \(X\) be a Banach space, \(Y\) a normed space and the nonlinear operator equation \(P\left( x\right) =0\), where…
On approximating the solutions of equations in metric spaces
Abstract Let \(\left( X,\rho \right)\) be a complete metric space, \(f:X\rightarrow X\) a nonlinear mapping. In order to solve the…
Error estimations in the numerical solving of the systems of equations
Abstract Let \(\left( x_{i},\rho_{i}\right) ,\ i=1,2,\) be two complete metric space and \(F_{1}:X_{1}\times X_{2}\rightarrow X_{1},\ F_{2}:X_{1}\times X_{2}\rightarrow X_{2}\) two nonlinear…