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.

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.

Orcid ID

http://orcid.org/0000-0002-5219-4869

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