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…
(original)
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…
An algorithm in the solving of equations by interpolation
Abstract Consider the nonlinear equation in \(R\), \(f\left( x\right) =0\), where \(f:A\rightarrow B \), \((A,B\subseteq \mathbb{R})\) which is assumed bijective. The Lagrange…
Error estimations in the numerical solving of systems of equations in metric spaces
Abstract Let \(X_{1},X_{2}\) be two complete metric spaces, \(X=X_{1}\times X_{2}\) and the nonlinear mappings \(F_{1}:X\rightarrow X_{1},\ F_{2}:X\rightarrow X_{2}\). In order…