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dc.contributor.authorBastounis, Alexander James
dc.date.accessioned2018-09-04T15:27:56Z
dc.date.available2018-09-04T15:27:56Z
dc.date.issued2018-10-20
dc.date.submitted2017-10-25
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279086
dc.description.abstractThis thesis is about computational theory in the setting of the mathematics of information. The first goal is to demonstrate that many commonly considered problems in optimisation theory cannot be solved with an algorithm if the input data is only known up to an arbitrarily small error (modelling the fact that most real numbers are not expressible to infinite precision with a floating point based computational device). This includes computing the minimisers to basis pursuit, linear programming, lasso and image deblurring as well as finding an optimal neural network given training data. These results are somewhat paradoxical given the success that existing algorithms exhibit when tackling these problems with real world datasets and a substantial portion of this thesis is dedicated to explaining the apparent disparity, particularly in the context of compressed sensing. To do so requires the introduction of a variety of new concepts, including that of a breakdown epsilon, which may have broader applicability to computational problems outside of the ones central to this thesis. We conclude with a discussion on future research directions opened up by this work.
dc.description.sponsorshipThis work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis.
dc.language.isoen
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectNumerical Analysis
dc.subjectMathematics of information
dc.subjectComputational Theory
dc.subjectHarmonic Analysis
dc.titleOn fundamental computational barriers in the mathematics of information
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentCambridge Centre for Analysis (CCA)
dc.date.updated2018-08-30T03:09:42Z
dc.identifier.doi10.17863/CAM.26466
dc.publisher.collegeChurchill College
dc.type.qualificationtitlePhD in Applied Mathematics at Cambridge Centre for Analysis
cam.supervisorHansen, Anders Christian
cam.thesis.fundingtrue
rioxxterms.freetoread.startdate2019-09-04


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