Solutions to inverse moment estimation problems in dimension 2, using best constrained approximation
| Autor: | Elodie Pozzi, Juliette Leblond |
|---|---|
| Přispěvatelé: | Analyse fonctionnelle pour la conception et l'analyse de systèmes (FACTAS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Saint Louis University (SLU) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
Inverse 010103 numerical & computational mathematics [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Regularization (mathematics) FOS: Mathematics Applied mathematics 0101 mathematics Divergence (statistics) Mathematics Numerical Analysis Partial differential equation Hardy spaces inverse problems Applied Mathematics Maxwell's equations and issues 010102 general mathematics Poisson-Laplace partial differential equation Poisson and Hilbert trans- forms Inverse problem Functional Analysis (math.FA) Mathematics - Functional Analysis Moment (mathematics) Sobolev space best constrained approximation and bounded extremal problems regularization Distribution (mathematics) Analysis |
| Zdroj: | Journal of Approximation Theory Journal of Approximation Theory, In press, ⟨10.1016/j.jat.2020.105520⟩ Journal of Approximation Theory, Elsevier, In press, ⟨10.1016/j.jat.2020.105520⟩ |
| ISSN: | 0021-9045 1096-0430 |
| DOI: | 10.1016/j.jat.2020.105520⟩ |
| Popis: | We study an inverse problem that consists in estimating the first (zero-order) moment of some R 2 -valued distribution m that is supported within a closed interval S ⊂ R , from partial knowledge of the solution to the Poisson–Laplace partial differential equation with source term equal to the divergence of m on another interval parallel to and located at some distance from S . Such a question coincides with a 2D version of an inverse magnetic “net” moment recovery question that arises in paleomagnetism, for thin rock samples. We formulate and constructively solve a best approximation problem under constraint in L 2 and in Sobolev spaces involving the restriction of the Poisson extension of the divergence of m . Numerical results obtained from the described algorithms for the net moment approximation are also furnished. |
| Databáze: | OpenAIRE |
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