An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption

DOI10.1088/0266-5611/23/1/011zbMath1118.65056OpenAlexW1995755093MaRDI QIDQ3425201

Shuai Lu, Ronny Ramlau, Sergei V. Pereverzyev

Publication date: 7 March 2007

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/23/1/011

zbMATH Keywords

numerical experimentserror boundnonlinear operator equationssource conditionminimal norm solutionbalancing principleadaptive parameter choice ruleoptimal rate convergence

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (14)

A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition ⋮ Direct instrumental nonparametric estimation of inverse regression functions ⋮ The minimal-norm Gauss-Newton method and some of its regularized variants ⋮ Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales ⋮ Tikhonov regularization for polynomial approximation problems in Gauss quadrature points ⋮ Regularization Methods for Ill-Posed Problems ⋮ Tikhonov regularization of nonlinear ill-posed equations under general source condition ⋮ A note on logarithmic convergence rates for nonlinear Tikhonov regularization ⋮ ON MOROZOV’S DISCREPANCY PRINCIPLE FOR NONLINEAR ILL-POSED EQUATIONS ⋮ Levenberg-Marquardt method with general convex penalty for nonlinear inverse problems ⋮ Nonlinear Tikhonov regularization in Hilbert scales with balancing principle tuning parameter in statistical inverse problems ⋮ About the Balancing Principle for Choice of the Regularization Parameter ⋮ On nonlinear ill-posed inverse problems with applications to pricing of defaultable bonds and option pricing ⋮ On convergence of regularized modified Newton's method for nonlinear ill-posed problems

Uses Software

• TIGRA

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