Dissertation
Algorithms for the unitary eigenvalue problem
Washington State University
Doctor of Philosophy (PhD), Washington State University
05/2007
DOI:
https://doi.org/10.7273/000005620
Abstract
Eigenvalues of unitary matrices arise in a variety of contexts in applied mathematics. This dissertation present four new algorithms for computing the eigenvalues of unitary matrices. In chapter 1, we give an overview these algorithms, and then survey the major applications where eigenvalues of unitary matrices arise. In chapter 2, we present the unitary QR algorithm, an algorithm that can used to compute all of the eigenvalues of a unitary matrix. In chapter 3, we present two Krylov space algorithms that approximate some of the eigenvalues of a large unitary matrix. Finally, in chapter 4, we present an algorithm that compute the eigenvalues of a unitary matrix U when U is expressed as a product U = U1 Un of unitary matrices of the same order. As a special case, we consider the generalized eigenvalue problem for unitary matrices.
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Details
- Title
- Algorithms for the unitary eigenvalue problem
- Creators
- Roden Jason A. David
- Contributors
- David S. Watkins (Chair)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 109
- Identifiers
- 99901054531001842
- Language
- English
- Resource Type
- Dissertation