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- W2019958605 abstract "In 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." @default.
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- W2019958605 date "2002-01-15" @default.
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- W2019958605 title "On the method of Lavrentiev regularization for nonlinear ill-posed problems" @default.
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- W2019958605 doi "https://doi.org/10.1088/0266-5611/18/1/313" @default.
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