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…
(original)
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 \(X\)…
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.…
On the efficiency of the computations for approximating the solutions of equations
Abstract We consider the iterative methods for solving nonlinear equations in \(\mathbb{R}\) and the class of iterative methods obtained by…
On some interpolatory iterative methods for the second degree polynomial operators (I)
Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…
On an approximation formula
Abstract 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)
Abstract 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 equations
Abstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…