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…
Numerical Analysis
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 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…
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…
Optimal algorithms concerning the solving of equations by interpolation
Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…
Error estimation in the numerical solving of operator equations
Abstract Let \(X\) be a Banach space and \(\varphi:X\rightarrow X\) a nonlinear operator. Assume the equation \(x=\varphi \left( x\right)\) has…
On the iterative methods with high convergence orders
Abstract Let \(X\) be a Banach space and \(Y\) a normed space, and \(P:X\rightarrow Y\) a nonlinear operator. In order…
Interpolation in linear normed spaces and applications
Abstract Let \(X,Y\) be two normed spaces and \(P:X\rightarrow Y\) a nonlinear operator. We construct the Lagrange interpolation operator for…
On interpolation with connected polynomials
Abstract We consider a function \(f\in C^{n-1}[a,b]\) and the nodes \(a=x_{0}<x_{1}<\ldots<x_{m}=b\). Given the values \begin{align}f\left( x_{i}\right) =&u_{i}, \quad i=1,…,m \\…