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On variational regularization: finite dimension and Hölder stability. (English) Zbl 1466.65039

Summary: In this paper, we analyze the convergence rates for finite-dimensional variational regularization in Banach spaces by taking into account the noisy data and operator approximations. In particular, we determine the convergence rates by incorporating the smoothness concepts of Hölder stability estimates and the variational inequalities. Additionally, we discuss two ill-posed inverse problems to complement the abstract theory presented in our main results.

MSC:

65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
49N45 Inverse problems in optimal control
65R32 Numerical methods for inverse problems for integral equations
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