Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind

DOI10.1080/01630568108816087zbMath0472.65045OpenAlexW2049791992MaRDI QIDQ3925809

Heinz W. Engl

Publication date: 1981

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630568108816087

zbMATH Keywords

Hilbert spaceiterative methodsill-posed problemregularization methodsMoore-Penrose generalized inversebounded linear operatorTikhonov's methodparameter choice strategyconditions for strong and weak convergence

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (14)

Convergence rates of iterated Tikhonov regularized solutions of nonlinear ill-posed problems ⋮ Theory and the methods of solution of ill-posed problems ⋮ On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems ⋮ On optimal convergence for regularized Tikhonov approximations ⋮ A posteriori parameter choice for general regularization methods for solving linear ill-posed problems ⋮ A parameter choice strategy for (iterated) tikhonov regularization of iii-posed problems leading to superconvergence with optimal rates ⋮ A deterministic approach to optimal regularization —The finite dimensional case— ⋮ Uniform convergence of regularization methods for linear ill-posed problems ⋮ On the asymptotic order of accuracy of Tikhonov regularization ⋮ Optimal order multilevel preconditioners for regularized ill-posed problems ⋮ The instability of some gradient methods for ill-posed problems ⋮ Stability estimates and regularization for an inverse heat conduction prolem in semi - infinite and finite time intervals ⋮ Continuity properties of the extension of a locally Lipschitz continuous map to the space of probability measures ⋮ Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates

Cites Work

• On rates of convergence for approximations to the generalized inverse
• On the Kryanev-Lardy Method for III-Posed Problems
• A numerical method for solving Fredholm integral equations of the 1st kind
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