On the error estimation in the numerical convergence of certain iterative methods7 years agoAbstract We study the nonlinear equations of the form x=\lambda D\left( x\right) +y, where \lambda \in \mathbb{R} and y\in E…
The convergence of certain iterative methods for solving certain operator equations7 years agoAbstract 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 method7 years agoAbstract 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 functions7 years agoAbstract 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 interpolation7 years agoAbstract 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 functions7 years agoAbstract 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 interpolation7 years agoAbstract 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 methods7 years agoAbstract 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 interpolation7 years agoAbstract 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 method7 years agoAbstract Let X be a Banach space, Y a normed space, P:X\rightarrow Y a nonlinear operator and the equation \(P\left(…