## 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…