Applications of the Modified Discrepancy Principle to Tikhonov Regularization of Nonlinear Ill-Posed Problems

DOI10.1137/S0036142997315470zbMath0970.65063MaRDI QIDQ4243574

Qi-nian Jin

Publication date: 19 May 1999

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergenceTikhonov regularizationdiscrepancy principlenonlinear ill-posed problemsdiffusion coefficientparameter estimationstwo point boundary value problem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Inverse problems for PDEs (35R30) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Inverse problems involving ordinary differential equations (34A55) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical solution to inverse problems in abstract spaces (65J22) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items (13)

Levenberg-Marquardt method in Banach spaces with general convex regularization terms ⋮ Parameter choices for sparse regularization with the ℓ1 norm ^* ⋮ The Levenberg-Marquardt regularization for the backward heat equation with fractional derivative ⋮ On variational regularization: finite dimension and Hölder stability ⋮ Selecting Regularization Parameters for Nuclear Norm--Type Minimization Problems ⋮ A fast adaptive algorithm for nonlinear inverse problems with convex penalty ⋮ A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems ⋮ Unnamed Item ⋮ A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles ⋮ A discrete scheme of Landweber iteration for solving nonlinear ill-posed problems ⋮ Tikhonov regularization of nonlinear ill-posed equations under general source condition ⋮ Dynamic force identification problem based on a novel improved Tikhonov regularization method ⋮ On a monotone ill-posed problem

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