Doctoral Dissertations
Date of Award
5-2020
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mathematics
Major Professor
Clayton Webster
Committee Members
Vasilios Alexiades, Michael Berry, Abner Salgado
Abstract
A major pillar of approximation theory in establishing the ability of one class of functions to be represented by another. Establishing such a relationship often leads to efficient numerical approximation methods. In this work, several expressibility theorems are established and several novel numerical approximation techniques are also presented. Not only are these novel methods supported by the presented theory, but also, provided numerical experiments show that these novel methods may be applied to a wide range of applications from image compression to the solutions of high-dimensional PDE.
Recommended Citation
Daws, Joseph Douglas Jr, "Applications of nonlinear approximation for problems in learning theory and applied mathematics. " PhD diss., University of Tennessee, 2020.
https://trace.tennessee.edu/utk_graddiss/5916
Comments
Portions of this document are under consideration for publication in the Proceedings of Machine Learning Research. Other portions are under consideration for publication in Signal Processing: Image Communication.