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(…
On the approximation of the solutions of equations in Banach spaces by sequences
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
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 nonlinear operator equations
Abstract Let \(X,Y\) be two Banach spaces and \(P:X\rightarrow Y\) a nonlinear operator. For solving the equation \(P\left( x\right) =0\)…
On some iterative methods for solving operator equations
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
Abstract Let \(X\) be a Banach space and \(\varphi:X\rightarrow X\) a nonlinear operator. Assume the equation \(x=\varphi \left( x\right)\) has…