On the iterative methods with high convergence orders
Abstract Let \(X\) be a Banach space and \(Y\) a normed space, and \(P:X\rightarrow Y\) a nonlinear operator. In order…
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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 =…
Multiscale structure of time series revealed by the monotony spectrum
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
Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…