Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
- 1 December 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 30 (6) , 1796-1838
- https://doi.org/10.1137/0730091
Abstract
The authors propose an a-posteriors strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems and show that under certain conditions, the convergence rate obtained with this strategy is optimal. As a by-product, a new stability estimate for the regularized solutions is given which applies to a class of parameter identification problems. The authors compare the parameter choice strategy with Morozov’s Discrepancy Principle. Finally, numerical results are presented.Keywords
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