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dc.contributor.authorIsakov, Victor, 1947-
dc.contributor.authorLu, Shuai
dc.contributor.authorXu, Boxi
dc.identifier.citationVictor Isakov, Shuai Lu, and Boxi Xu Linearized Inverse Schrödinger Potential Problem at a Large Wavenumber SIAM Journal on Applied Mathematics 2020 80:1, 338-358en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractWe investigate recovery of the (Schrodinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Holder type stability which is a big improvement over a logarithmic stability in low wavenumbers. Furthermore we extend the discussion to the linearized inverse Schrodinger potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of the Fourier modes of the potential function. By choosing the large wavenumber appropriately, we verify the efficiency of the proposed algorithm by several numerical examples.en_US
dc.description.sponsorshipEmylou Keith and Betty Dutcher Distinguished Professorship and the NSF grant DMS 15-14886. The work of the second author was supported by NSFC 11925104 and by the Shanghai Municipal Education Commission 16SG01. The work of the third author was supported by NSFC 11801351 and by the Shanghai Pujiang Program 18PJ1403600.en_US
dc.publisherSociety for Industrial and Applied Mathematics Publicationsen_US
dc.relation.ispartofseriesSIAM Journal on Applied Mathematics;v.80:no.1
dc.subjectInverse boundary value problemen_US
dc.subjectSchrödinger potential problemen_US
dc.subjectStability estimateen_US
dc.titleLinearized inverse Schrödinger potential problem at a large wavenumberen_US
dc.rights.holder© 2020 SIAMen_US

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