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…

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

Book summaryTo be completed. AuthorIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy TitleOriginal title (in Romanian) Introducere în…

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…