Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations

DOI10.1553/etna_vol58s450zbMath1521.65046OpenAlexW4382994579MaRDI QIDQ6076064

Publication date: 21 September 2023

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2021-2030/vol58/abstract.php?vol=58&pages=450-469

zbMATH Keywords

nonlinear ill-posed problems Lavrentiev regularization heuristic parameter choice rules

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)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Lavrentiev's regularization method in Hilbert spaces revisited
Lavrentiev regularization of nonlinear ill-posed problems
On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems
On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
Lavrentiev regularization for linear ill-posed problems under general source conditions
On the iteratively regularized Gauss-Newton method in Banach spaces with applications to parameter identification problems
Lavrentiev regularization and balancing principle for solving ill-posed problems with monotone operators
A posteriori stopping rule for regularized fixed point iterations
On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations
Hanke-Raus heuristic rule for variational regularization in Banach spaces
Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle
ITERATED LAVRENTIEV REGULARIZATION FOR NONLINEAR ILL-POSED PROBLEMS
Iterative Regularization and Generalized Discrepancy Principle for Monotone Operator Equations
Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
Applicability of the disparity principle in the case of non-linear incorrectly posed problems, and a new regularizing algorithm for solving them
Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
On the method of Lavrentiev regularization for nonlinear ill-posed problems
On the choice of the regularization parameter for ordinary and iterated Tikhonov regularization of nonlinear ill-posed problems
Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule
ON APPLICATION OF GENERALIZED DISCREPANCY PRINCIPLE TO ITERATIVE METHODS FOR NONLINEAR ILL-POSED PROBLEMS
Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces
Weakly closed nonlinear operators and parameter identification in parabolic equations by tikhonov regularization
A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems
Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates
A numerical study of heuristic parameter choice rules for total variation regularization
Analysis of a generalized regularized Gauss–Newton method under heuristic rule in Banach spaces

This page was built for publication: Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations