We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these sequences resulted as accelerated iterations toward a fixed point. We give here a Kantorovich-type result, which provides sufficient conditions ensuring the convergence of the accelerated iterates.
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
fixed point; successive approximations; accelerated successive approximations; nonlinear system of equations in Rn; inexact Newton method; perturbed Newton method; ; local convergence; convergence order.
Latex-pdf version of the paper.
E. Cătinaş, Sufficient convergence conditions for certain accelerated successive approximations. In: Mache D.H., Szabados J., de Bruin M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151, pp. 71-75, 2005. Birkhäuser Basel
Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151.