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Linear ill-posed problems written as the operator equation A = on sets of functions z convex on multi-dimensional sets Ω are considered in the paper. A regularizing algorithm z η = R ( A h , u δ , η ), where || A h − A || ≤ h , || u δ − || ≤ δ , η = ( h , δ ), obtained in the...
Finding the derivative of a (discrepancy) functional under minimization is an important stage in the analysis of inverse and optimization problems. This problem becomes even more complicated if the state equation involves a nonsmooth operator. The encountered difficulties can be resolved by...
We describe two regularization techniques based on optimal control for solving two types of ill-posed problems. We include convergence proofs of the regularization method and error estimates. We illustrate our method through problems in signal processing and parameter identification using an...
In this paper we treat a new regularization method which is well-suited for ill-posed problems with discontinuous solutions: adaptive grid regularization . After describing the method we present several numerical examples showing that this method is a powerful tool to identify discontinuities in...
An inverse contact problem is a classical ill-posed problem in the sense of Hadamard. In this paper we develop a numerical computational method for solving an inverse contact problem in elasticity. Based on the Tikhonov regularization technique, we transform the original problem into an...
We study the global stability in determination of multiple coefficients of terms of highest order in an acoustic equation with Dirichlet boundary data. Under regular initial data, we prove the uniqueness and a Hölder stability estimate in the inverse problem with some observations on a suitable...
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