Degree Type

Dissertation

Date of Award

2017

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Irvin Hentzel

Second Advisor

Sung Song

Abstract

This paper explores the nature and application of minimal-support solutions of underdetermined systems of linear equations. First, methods for directly solving the problem are evaluated for effectiveness, and cases are shown to demonstrate that these direct methods are unreliable for finding minimal support solutions. The NP-Hardness of minimal-support solution recovery is then demonstrated over any field for the first time in the literature, and further NP-Hardness results are explored after this presentation. Following these expositions, a summary of current techniques in the practice of Compressive Sensing is given, and a novel method for comprehensively solving minimal-support solutions of underdetermined systems over any field is stated, discussed and proven. A summary of findings and avenues for future opportunities concludes the dissertation.

Copyright Owner

Darrin Thomas Rasberry

Language

en

File Format

application/pdf

File Size

82 pages

Included in

Mathematics Commons

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