Abstract
In this paper we start with the consideration of a parameter estimation problem with noisy data which arises as an inverse problem in groundwater filtration. It turns out that in appropriate Hilbert spaces this problem can be formulated as a linear non-compact ill-posed problem with a model perturbation that can be estimated only at the solution of the problem. In the remaining part of the paper we deal with those problems in general Hilbert spaces and consider the CGNR method, this is, the classical method of conjugate gradients by Hestenes and Stiefel applied to the associated normal equations. Two a posteriori stopping rules are introduced to obtain stable numerical solutions, and convergence results are provided for the corresponding approximations, respectively. Finally, being a main concern of this paper, we present numerical illustrations with the CGNR method applied to a non-compact linear perturbed test problem.
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Dedicated to the memory of Professor Siegfried Prößdorf
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Plato, R. (2001). On an inverse problem in groundwater filtration and its regularization by the conjugate gradient method. In: Elschner, J., Gohberg, I., Silbermann, B. (eds) Problems and Methods in Mathematical Physics. Operator Theory: Advances and Applications, vol 121. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8276-7_21
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DOI: https://doi.org/10.1007/978-3-0348-8276-7_21
Publisher Name: Birkhäuser, Basel
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