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

Function 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Computer Science and Applications

Department dc:contributor.department

Computer Science

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2020

Author dc:creator

• Lux, Thomas Christian Hansen

Chairs dc:contributor.committeechair

• Watson, Layne T.
• Hong, Yili

Committee members dc:contributor.committeemember

• Wang, Gang Alan
• Cameron, Kirk W.
• Huang, Bert
• Cao, Young

• Approximation Theory
• Numerical Analysis
• High Performance Computing
• Computer Security
• Nonparametric Statistics
• Mathematical Software

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:27379

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/100059