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  4. Regularized Kernel-Based Reconstruction in Generalized Besov Spaces
 
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2018
  • Zeitschriftenaufsatz

Titel

Regularized Kernel-Based Reconstruction in Generalized Besov Spaces

Abstract
We present a theoretical framework for reproducing kernel-based reconstruction methods in certain generalized Besov spaces based on positive, essentially self-adjoint operators. An explicit representation of the reproducing kernel is given in terms of an infinite series. We provide stability estimates for the kernel, including inverse Bernstein-type estimates for kernel-based trial spaces, and we give condition estimates for the interpolation matrix. Then, a deterministic error analysis for regularized reconstruction schemes is presented by means of sampling inequalities. In particular, we provide error bounds for a regularized reconstruction scheme based on a numerically feasible approximation of the kernel. This allows us to derive explicit coupling relations between the series truncation, the regularization parameters and the data set.
Author(s)
Griebel, Michael
Rieger, Christian
Zwicknagl, Barbara
Zeitschrift
Foundations of Computational Mathematics
Funder
Deutsche Forschungsgemeinschaft DFG
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DOI
10.1007/s10208-017-9346-z
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Language
Englisch
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