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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).

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

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Abstract

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
Language:English
edoc DOI:
Last Modified:14 Jan 2022 07:05
Deposited On:14 Jan 2022 07:05

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