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…
Solving the systems of operator equations by iterative methods
Abstract Let \(X,Y\) be two Banach spaces and \(Z=X\times Y\). We consider the system of nonlinear equations \[x=\varphi \left( x,y\right),\\…
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 \\…
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 =…
On an Aitken type method
Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…