Type of Document Master's Thesis Author Johnson, Paul D. Author's Email Address oaktreebakery@hotmail.com URN etd-11192008-201133 Title Factorization of Quasiseparable Matrices Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Michael Stewart Committee Chair Frank Hall Committee Member George Davis Committee Member Keywords
- QR factorization
- fast algorithms
- quasiseparable matrices
- structure matrices
Date of Defense 2008-11-04 Availability unrestricted Abstract This paper investigates some of the ideas and algorithms developed for exploiting the structure of quasiseparable matrices. The case of purely scalar generators is considered initially. Theprocess by which a quasiseparable matrix is represented as the product of matrices comprised of its generators is explained. This is done clearly in the scalar case, but may be extended to block generators. The complete factoring approach is then considered. This consists of two stages: inner-outer factorization followed by inner-coprime factorization. Finally, the stability of the algorithm is investigated. The algorithm is used to factor various quasiseparable matrices R created first using minimal generators, and subsequently using non-minimal generators. The result is that stability of the algorithm is compromised when non-minimal generators are present.
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