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 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…
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 \\…
Introduction to the theory of approximating the solutions of equations
About this book To be completed. Author Ion Păvăloiu Title Original title (in Romanian) Introducere în teoria aproximarii soluțiilor ecuațiilor…
Remarks on solving the systems of equations by iterative methods
Abstract In this paper we give a condition for the convergence of an iterative method of Gauss-Seidel type \[ x_i =…