An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
-
Santhosh George
und
Suresan Pareth
Abstract.
Motivated by the two-step directional Newton method
considered by Argyros and Hilout (2010) for approximating a zero 
of a
differentiable function F defined on a convex set 
of
a Hilbert space H, 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 X. 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 x0 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.
© 2013 by Walter de Gruyter Berlin Boston
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- Masthead
- A characterization of pseudo-Einstein real hypersurfaces of a complex space form
- An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
- Topological conjugation to uniformly piecewise linear transformations
- Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
- An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain
- Nondifferentiable (Φ,ρ)-type I and generalized (Φ,ρ)-type I functions in nonsmooth vector optimization
- An optimal double inequality between logarithmic and generalized logarithmic means
- A further generalization of the 𝒯𝒜d-density topology
- Erratum Bloch varieties of higher-dimensional, periodic Schrödinger operators [J. Appl. Anal. 15 (2009), 33–46]
Artikel in diesem Heft
- Masthead
- A characterization of pseudo-Einstein real hypersurfaces of a complex space form
- An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
- Topological conjugation to uniformly piecewise linear transformations
- Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
- An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain
- Nondifferentiable (Φ,ρ)-type I and generalized (Φ,ρ)-type I functions in nonsmooth vector optimization
- An optimal double inequality between logarithmic and generalized logarithmic means
- A further generalization of the 𝒯𝒜d-density topology
- Erratum Bloch varieties of higher-dimensional, periodic Schrödinger operators [J. Appl. Anal. 15 (2009), 33–46]
