Titelaufnahme

Titel
A semismooth Newton method for nonlinear parameter identification problems with impulsive noise
Verfasser/ VerfasserinClason, Christian ; Jin, Bangti
Erschienen in
SIAM journal on imaging sciences / Society for Industrial and Applied Mathematics, Philadelphia, Pa. : SIAM, 1.2008 -, Jg. 5, H. 2, S. 505-538
ErschienenSIAM
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)semismooth Newton method / parameter identification / impulsive noise / L1 data fitting / regularization parameter / noise model
ISSN1936-4954
URNurn:nbn:at:at-ubg:3-266 Persistent Identifier (URN)
DOIdoi:10.1137/110826187 
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A semismooth Newton method for nonlinear parameter identification problems with impulsive noise [2.69 mb]
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Zusammenfassung (Englisch)

This work is concerned with nonlinear parameter identification in partial differential equations subjectto impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model withL1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging.By approximating this problem using a family of smoothed functionals, a semismooth Newtonmethod becomes applicable. In particular, its superlinear convergence is proved under a second-ordercondition. The convergence of the solution to the approximating problem as the smoothing parametergoes to zero is shown. A strategy for adaptively selecting the regularization parameter basedon a balancing principle is suggested. The efficiency of the method is illustrated on several benchmarkinverse problems of recovering coefficients in elliptic differential equations, for which one- andtwo-dimensional numerical examples are presented.

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