On minimal support solutions of underdetermined systems of linear equations

dc.contributor.advisor Irvin Hentzel
dc.contributor.advisor Sung Song
dc.contributor.author Rasberry, Darrin
dc.contributor.department Mathematics
dc.date 2018-08-11T12:12:23.000
dc.date.accessioned 2020-06-30T03:03:40Z
dc.date.available 2020-06-30T03:03:40Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 2017
dc.date.embargo 2001-01-01
dc.date.issued 2017-01-01
dc.description.abstract <p>This paper explores the nature and application of minimal-support solutions of underdetermined systems of linear equations. First, methods for directly solving the problem are evaluated for effectiveness, and cases are shown to demonstrate that these direct methods are unreliable for finding minimal support solutions. The NP-Hardness of minimal-support solution recovery is then demonstrated over any field for the first time in the literature, and further NP-Hardness results are explored after this presentation. Following these expositions, a summary of current techniques in the practice of Compressive Sensing is given, and a novel method for comprehensively solving minimal-support solutions of underdetermined systems over any field is stated, discussed and proven. A summary of findings and avenues for future opportunities concludes the dissertation.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/etd/15405/
dc.identifier.articleid 6412
dc.identifier.contextkey 11054571
dc.identifier.doi https://doi.org/10.31274/etd-180810-5029
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/15405
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/29588
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/etd/15405/Rasberry_iastate_0097E_16475.pdf|||Fri Jan 14 20:40:40 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Compressive
dc.subject.keywords Minimal
dc.subject.keywords Sensing
dc.subject.keywords Support
dc.title On minimal support solutions of underdetermined systems of linear equations
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.discipline Mathematics
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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