Lux, Thomas Christian Hansen2020-09-242020-09-242020-09-23vt_gsexam:27379http://hdl.handle.net/10919/100059Function 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.ETDIn CopyrightApproximation TheoryNumerical AnalysisHigh Performance ComputingComputer SecurityNonparametric StatisticsMathematical SoftwareDissertation