Publication Date
2017
Document Type
Thesis
Committee Members
Yuqing Chen (Committee Member), Weifu Fang (Committee Member), Sara Pollock (Advisor)
Degree Name
Master of Science (MS)
Abstract
In this thesis, we are investigating the solutions λ of a typical quadratic eigenvalue problem (QEP). Indeed, solutions [lambda] of a QEP of the form Q([lambda])=[lambda]2M+[lambda]D+S that satisfy Q([lambda])=0, can be obtained iteratively and without linearizing the problem. However, many iterative methods can only find some of the solutions [lambda]. Therefore, we are going to modify a method based on Newton iterations in order to find all of the solutions [lambda], that are known also as the eigenvalues of the QEP. In addition, we will investigate how the proposed method compares with standard iterative methods from the literature. Moreover, we will provide a method for finding an upper bound for the number of the eigenvalues of the QEP, and apply this in our method for the purpose of finding all solutions [lambda].
Page Count
66
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
2017
Copyright
Copyright 2017, some rights reserved. My ETD may be copied and distributed only for non-commercial purposes and may not be modified. All use must give me credit as the original author.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
ORCID ID
0000-0003-2959-4212
