Convergence rates of iterated Tikhonov regularized solutions of nonlinear ill-posed problems

DOI10.1007/BF01385697zbMath0791.65040MaRDI QIDQ1326481

Otmar Scherzer

Publication date: 7 July 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133762

zbMATH Keywords

numerical examplesinverse problemsparameter identificationconvergence ratenonlinear ill-posed problemsiterated Tikhonov regularization

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (11)

Convergence rates of regularized solutions of nonlinear ill-posed operator equations involving monotone operators ⋮ Multiple level sets for piecewise constant surface reconstruction in highly ill-posed problems ⋮ On inertial iterated Tikhonov methods for solving ill-posed problems ⋮ A new Kaczmarz-type method and its acceleration for nonlinear ill-posed problems ⋮ Tikhonov-like methods with inexact minimization for solving linear ill-posed problems ⋮ On a Family of Gradient-Type Projection Methods for Nonlinear Ill-Posed Problems ⋮ A generalization of continuous regularized Gauss–Newton method for ill-posed problems ⋮ On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations ⋮ Modern regularization methods for inverse problems ⋮ The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems ⋮ On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations

Cites Work

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• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation
• Stability for parameter estimation in two point boundary value problems.
• Approximation of generalized inverses by iterated regularization
• Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind
• Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems

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