On the superlinear convergence of the successive approximations method
Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…
2002
Affine invariant conditions for the inexact perturbed Newton method
Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…
On the approximation of solutions to nonlinear operators between metric spaces
Abstract A Gauss-Seidel method for linear systems, based on decomposing the matrix system into four submatrices blocks, has been proposed…
On a third order iterative method for solving polynomial operator equations
Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…
Aitken-Steffensen-type methods for nonsmooth functions (II)
Abstract We present some new conditions which assure that the Aitken-Steffensen method yields bilateral approximation for the solution of a…
Aitken-Steffensen-type methods for nondifferentiable functions (I)
Abstract We study the convergence of the Aitken-Steffensen method for solving a scalar equation \(f(x)=0\). Under reasonable conditions (without assuming…