Error Estimates for Adaptive Spectral Decompositions

Baffet, Daniel H. and Gleichmann, Yannik G. and Grote, Marcus J.. (2022) Error Estimates for Adaptive Spectral Decompositions. Preprints Fachbereich Mathematik, 2022 (01).


Official URL: https://edoc.unibas.ch/86739/

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Adaptive spectral (AS) decompositions associated with a piecewise constant function, $u$, yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods, AS decompositions have proved remarkably efficient in providing at each nonlinear iteration a low-dimensional search space for the solution of inverse medium problems. Here, we derive $L^2$-error estimates for the AS decomposition of $u$, truncated after $K$ terms, when $u$ is piecewise constant and consists of $K$ characteristic functions over Lipschitz domains and a background. Numerical examples illustrate the accuracy of the AS decomposition for media that either do, or do not, satisfy the assumptions of the theory.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Baffet, Daniel Henri and Gleichmann, Yannik G. and Grote, Marcus J.
Item Type:Preprint
Publisher:Universität Basel
edoc DOI:
Last Modified:14 Jan 2022 07:05
Deposited On:14 Jan 2022 07:05

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