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On some iterative methods for solving operator equations

8 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

8 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

8 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

8 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

8 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

8 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

8 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

8 years ago

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

Multiscale structure of time series revealed by the monotony spectrum

9 years ago

AbstractObservation of complex systems produces time series with specific dynamics at different time scales. The majority of the existing numerical…

On an Aitken type method

18 years ago

Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…

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