U Tautenhahn 2002 Inverse Problems 18 191 doi:10.1088/0266-5611/18/1/313
On the method of Lavrentiev regularization for nonlinear ill-posed problems
U Tautenhahn
Show affiliationsIn this paper we study the method of Lavrentiev regularization to reconstruct solutions x† of nonlinear ill-posed problems F (x) = y where instead of y noisy data yδ 
X with || y − yδ|| ≤ δ are given and F : D(F) ⊂ X → X is a monotone nonlinear operator. In this regularization method regularized solutions xαδ are obtained by solving the singularly perturbed nonlinear operator equation F (x) + α(x−
) = yδ with some initial guess . Assuming certain conditions concerning the nonlinear operator F and the smoothness of the element −x† we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly.
- PACS
- MSC
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47H05 Monotone operators (with respect to duality)
- Subjects
- Dates
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Issue 1 (February 2002)
Received 22 May 2001, in final form 14 September 2001
Published 15 January 2002
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On the method of Lavrentiev regularization for nonlinear ill-posed problems
U Tautenhahn 2002 Inverse Problems 18 191
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