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On the approximation of the solutions of equations in Banach spaces by sequences

9 years ago

Abstract Let \(X\) be a Banach space, \(Y\) a normed space \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left(…

On the convergence of a class of iteration methods of J. F. Traub

9 years ago

Abstract Let \(X\) be a Banach space, \(Y\) a normed space and \(P:X\rightarrow Y\) a nonlinear operator. We study the…

On some iterative methods for solving operator equations

9 years ago

Abstract Let \(X,Y\) be two Banach spaces and \(P:X\rightarrow Y\) a nonlinear operator. We study the semilocal convergence of the…

Error estimation in the numerical solving of operator equations

9 years ago

Abstract Let \(X\) be a Banach space and \(\varphi:X\rightarrow X\) a nonlinear operator. Assume the equation \(x=\varphi \left( x\right)\) has…

Considerations regarding the iterative methods obtained by inverse interpolation

9 years ago

Abstract Let \(X,Y\) be two normed spaces and \(P:X\rightarrow Y\) a nonlinear operator. We consider the generalized inverse interpolation polynomial and…

On iterated operators

9 years ago

Abstract Let \(X,Y\) be normed spaces and \(F:X\rightarrow Y\) a nonlinear operator. Let \(Q:X\rightarrow X.\) We study the convergence orders of…

On the iterative methods with high convergence orders

9 years ago

Abstract Let \(X\) be a Banach space and \(Y\) a normed space, and \(P:X\rightarrow Y\) a nonlinear operator. In order…

Solving the systems of operator equations by iterative methods

9 years ago

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

9 years ago

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

9 years ago

Abstract In this paper we give a condition for the convergence of an iterative method of Gauss-Seidel type \[ x_i =…

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