Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess

DOI10.1515/jiip.2011.024zbMath1279.35113OpenAlexW1967244488MaRDI QIDQ5745451

Larisa Beilina, Michael V. Klibanov, Anatoly B. Bakushinsky

Publication date: 30 January 2014

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2011.024

zbMATH Keywords

uniqueness theoremTikhonov functionala single value of the level of error

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Inverse problems in optimal control (49N45)

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Cites Work

• Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
• Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D
• Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm
• Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem
• Carleman estimates for parabolic equations and applications
• Inverse problems and Carleman estimates
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• Inverse problems for a perturbed dissipative half-space
• A Globally Convergent Numerical Method for a Coefficient Inverse Problem
• Lipschitz stability of an inverse problem for an acoustic equation