Sufficient convergence conditions for certain accelerated successive approximations

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.

Emil Cătinaş
(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.

Scanned paper.

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

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