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Browsing Auburn Theses and Dissertations by Author "Oeding, Luke"

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Applications of Stochastic Gradient Descent for Optimization of Complex Systems with Uncertainty 

Das, Somak (2021-07-27)
The Stochastic Gradient Descent (SGD) method in all its variations has gained popularity with the recent progress in Machine learning. In this dissertation we implement and analyze two modifications of the SGD method. In ...

Determinants of Sums of Normal Matrices 

Speck, Matthew (2024-05-06)  ETD File Embargoed
Recent efforts in matrix theory have been concerned with describing invariants of matrices with "nice" properties. In this dissertation, we address a conjecture on the determinant of the sum of a pair of normal matrices. ...

Extensions of Monotonicity Results to Semisimple Lie Groups 

Sarver, Zachary (2016-05-05)
We extend a monotonicity result of Wang and Gong on the product of powers of positive definite matrices. This result concerns the eigenvalues of such products which written as vectors have a log majorization relationship. ...

Intersection Structures on Secants of Grassmannians 

Bidleman, Dalton (2023-08-02)  ETD File Embargoed
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k-planes with the restriction that their intersection has a prescribed dimension. This thesis calculates dimensions of ...

An Introduction to Bernstein-Gel’fand-Gel’fand Correspondence 

Dixon, Robert (2022-08-04)
This master's thesis serves as an introduction to the Bernstein-Gel'fand-Gel'fand correspondence first written in 1978. We shall cover some of the fundamental objects that the reader may not be familiar with, mainly tensor ...

The Utilization of Geometric Hashing Techniques for Feature Association during Ground Vehicle Localization 

Sprunk, Michael (2023-04-28)
This thesis presents a new approach to laser-based robot localization using the concept of geometric hashing. The technique operates on an a priori feature map representing the navigation environment by recording all ...