On the error estimation in the numerical convergence of certain iterative methods
Abstract We study the nonlinear equations of the form \[x=\lambda D\left( x\right) +y,\] where \(\lambda \in \mathbb{R}\) and \(y\in E\)…
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The convergence of certain iterative methods for solving certain operator equations
Abstract We consider the solving of the equation \[x=\lambda D\left( x\right)+y,\] where \(E\) is a Banach space and \(D:E\rightarrow E\), \(\lambda\in…
A generalization of the Newton method
Abstract Let \(X\) be a Banach space, \(Y\) a normed space, \(G:X\rightarrow Y\) a nonlinear operator, and \(G\left( x\right) =0\)…
Solving equations with the aid of inverse rational interpolation functions
Abstract We study the convergence of an iterative method for solving the equation \(f\left( x\right) =0,\ f:A\rightarrow B\), \(A,B\subseteq \mathbb{R}\), \(f\)…
Solving equations by Hermite type inverse interpolation
Abstract We study the convergence of an iterative method for solving the equation (fleft( xright) =0, f:Isubseteq mathbb{Rrightarrow R}). The…
Solving equations with the aid of inverse interpolation spline functions
Abstract We consider the solving of a nonlinear equation in \(\mathbb{R}\). We construct a spline function which approximates the nonlinear…
Optimal Steffensen type iterative methods obtained by inverse interpolation
Abstract Let \(f:I\subset \mathbb{R\rightarrow R}\) be a nonlinear mapping and the equation \(f\left( x\right) =0\) with solution \(x^{\ast}\); consider the…
On optimal iterative methods
Abstract Let \(\left( X,\rho \right)\) be a complete matrix space, the nonlinear mapping \(\varphi:I\subset X\rightarrow X\) and the equation \(x=\varphi…
Solving equations by interpolation
Abstract Let \(X,Y\) be normed spaces, \(G:X\rightarrow Y\) a nonlinear operator, and the nonlinar equation \(G\left( x\right) =0\). We define…
A variant of the Newton method
Abstract Let \(X\) be a Banach space, \(Y\) a normed space, \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left(…