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Factorization of Quasiseparable Matrices

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. The process 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.

Identiferoai:union.ndltd.org:GEORGIA/oai:digitalarchive.gsu.edu:math_theses-1064
Date21 November 2008
CreatorsJohnson, Paul D.
PublisherDigital Archive @ GSU
Source SetsGeorgia State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMathematics Theses

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