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dc.contributor.advisorSantosh Vempala.en_US
dc.contributor.authorDunagan, John D. (John David), 1976-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2005-08-23T19:51:41Z
dc.date.available2005-08-23T19:51:41Z
dc.date.copyright2002en_US
dc.date.issued2002en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/8396
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.en_US
dc.descriptionIncludes bibliographical references (p. 91-94).en_US
dc.description.abstractWe develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a high-dimensional data set and show the algorithm to be asymptotically good. We extend this result to distributions that we can access only by sampling, and also to the optimization version of the problem. Our results cover both the discrete and continuous cases. This is joint work with Santosh Vempala. The complexity of solving linear programs has interested researchers for half a century now. We show that an arbitrary linear program subject to a small random relative perturbation has good condition number with high probability, and hence is easy to solve. This is joint work with Avrim Blum, Daniel Spielman, and Shang-Hua Teng. This result forms part of the smoothed analysis project initiated by Spielman and Teng to better explain mathematically the observed performance of algorithms.en_US
dc.description.statementofresponsibilityby John D. Dunagan.en_US
dc.format.extent94 p.en_US
dc.format.extent7211412 bytes
dc.format.extent7211171 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleA geometric theory of outliers and perturbationen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc50594675en_US


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