Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems
- 1 January 1990
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 11 (1-2) , 85-99
- https://doi.org/10.1080/01630569008816362
Abstract
In this paper we consider non-linear ill-posed problems F(x)=y0 in a Hilbert space setting. We solve these problems with Tikhonov regularization combined with finite-dimensional approximation where the data y0 and the non-linear operator F are assumed to be known only approximately. Conditions are given that guarantee optimal convergence rates with respect to both, the data noise and the finite-dimensional approximation. Finally, we present some numerical results for parameter estimation problems that verify the theoretical results.Keywords
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