Interpolants, Error Bounds, and Mathematical Software for Modeling and Predicting Variability in Computer Systems

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dc.contributor.authorLux, Thomas Christian Hansenen
dc.contributor.committeechairWatson, Layne T.en
dc.contributor.committeechairHong, Yilien
dc.contributor.committeememberWang, Gang Alanen
dc.contributor.committeememberCameron, Kirk W.en
dc.contributor.committeememberHuang, Berten
dc.contributor.committeememberCao, Youngen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2020-09-24T08:00:29Zen
dc.date.available2020-09-24T08:00:29Zen
dc.date.issued2020-09-23en
dc.description.abstractFunction approximation is an important problem. This work presents applications of interpolants to modeling random variables. Specifically, this work studies the prediction of distributions of random variables applied to computer system throughput variability. Existing approximation methods including multivariate adaptive regression splines, support vector regressors, multilayer perceptrons, Shepard variants, and the Delaunay mesh are investigated in the context of computer variability modeling. New methods of approximation using Box splines, Voronoi cells, and Delaunay for interpolating distributions of data with moderately high dimension are presented and compared with existing approaches. Novel theoretical error bounds are constructed for piecewise linear interpolants over functions with a Lipschitz continuous gradient. Finally, a mathematical software that constructs monotone quintic spline interpolants for distribution approximation from data samples is proposed.en
dc.description.abstractgeneralIt is common for scientists to collect data on something they are studying. Often scientists want to create a (predictive) model of that phenomenon based on the data, but the choice of how to model the data is a difficult one to answer. This work proposes methods for modeling data that operate under very few assumptions that are broadly applicable across science. Finally, a software package is proposed that would allow scientists to better understand the true distribution of their data given relatively few observations.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:27379en
dc.identifier.urihttp://hdl.handle.net/10919/100059en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectApproximation Theoryen
dc.subjectNumerical Analysisen
dc.subjectHigh Performance Computingen
dc.subjectComputer Securityen
dc.subjectNonparametric Statisticsen
dc.subjectMathematical Softwareen
dc.titleInterpolants, Error Bounds, and Mathematical Software for Modeling and Predicting Variability in Computer Systemsen
dc.typeDissertationen
thesis.degree.disciplineComputer Science and Applicationsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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