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An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
Ist Teil von
Journal of applied analysis, 2013-12, Vol.19 (2), p.181-196
Ort / Verlag
Berlin: Walter de Gruyter GmbH
Erscheinungsjahr
2013
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Motivated by the two-step directional Newton method
considered by Argyros and Hilout (2010) for approximating a zero
of a
differentiable function
defined on a convex set
of
a Hilbert space
, we consider a two-step Newton–Lavrentiev method
(TSNLM) for obtaining an approximate solution to the nonlinear
ill-posed operator equation
, where
is a nonlinear monotone operator defined on a real
Hilbert space
. It is assumed that
and that the
only available data are
with
.
We prove that the TSNLM converges cubically to a solution of the
equation
(such solution is an approximation of
)
where
is the initial guess. Under a general source condition
on
, we derive order optimal error bounds by choosing
the regularization parameter α according to the balancing
principle considered by Perverzev and Schock (2005). The
computational results provided endorse the reliability and
effectiveness of our method.