Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates
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Publication:1071480
DOI10.1007/BF00941281zbMath0586.65045OpenAlexW2036695884MaRDI QIDQ1071480
Publication date: 1987
Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00941281
noisy dataTikhonov regularizationdiscrepancy principleoptimal convergence ratesleast-square solutiona posteriori parameter choice strategiesill- posedminimal-norm
Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Parameter choice by discrepancy principles for the approximate solution of ill-posed problems
- Asymptotic convergence rate of arcangeli's method for III-posed problems
- Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind
- On the asymptotic order of accuracy of Tikhonov regularization
- On the asymptotic order of accuracy of Tikhonov regularization
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