Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential
dc.contributor.author | Yagle, Andrew E. | en_US |
dc.date.accessioned | 2006-12-19T19:14:46Z | |
dc.date.available | 2006-12-19T19:14:46Z | |
dc.date.issued | 1998-06-01 | en_US |
dc.identifier.citation | Yagle, Andrew E (1998). "Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential ." Inverse Problems. 14(3): 763-778. <http://hdl.handle.net/2027.42/49103> | en_US |
dc.identifier.issn | 0266-5611 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/49103 | |
dc.description.abstract | We develop discrete counterparts to the Gel'fand-Levitan and Marchenko integral equations for the two-dimensional (2D) discrete inverse scattering problem in polar coordinates with a nonlocal potential. We also develop fast layer stripping algorithms that solve these systems of equations exactly. The significance of these results is: (1) they are the first numerical implementation of Newton's multidimensional inverse scattering theory; (2) they show that the result will almost always be a nonlocal potential, unless the data are `miraculous'; (3) they show that layer stripping algorithms implement fast `split' signal processing fast algorithms; (4) they link 2D discrete inverse scattering with 2D discrete random field linear least-squares estimation; and (5) they formulate and solve 2D discrete Schrödinger equation inverse scattering problems in polar coordinates. | en_US |
dc.format.extent | 3118 bytes | |
dc.format.extent | 168389 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.publisher | IOP Publishing Ltd | en_US |
dc.title | Discrete Gel'fand-Levitan and Marchenko matrix equations and layer stripping algorithms for the discrete two-dimensional Schrödinger equation inverse scattering problem with a nonlocal potential | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109-2122, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/49103/2/ip8322.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1088/0266-5611/14/3/023 | en_US |
dc.identifier.source | Inverse Problems. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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