Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices

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dc.contributor.authorFang, Haw-ren
dc.contributor.authorO'Leary, Dianne
dc.date.accessioned2006-01-13T22:16:05Z
dc.date.available2006-01-13T22:16:05Z
dc.date.issued2006-01-13T22:16:05Z
dc.description.abstractWe call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider $LXL^T$ factorizations of symmetric triadic matrices, where $L$ is unit lower triangular and $X$ is diagonal, block diagonal with $1\!\times\!1$ and $2\!\times\!2$ blocks, or the identity with $L$ lower triangular. We prove that with diagonal pivoting, the $LXL^T$ factorization of a symmetric triadic matrix is sparse, study some pivoting algorithms, discuss their growth factor and performance, analyze their stability, and develop perturbation bounds. These factorizations are useful in computing inertia, in solving linear systems of equations, and in determining modified Newton search directions.en
dc.format.extent220072 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/3040
dc.language.isoen_USen
dc.relation.ispartofseriesUM Computer Science Departmenten
dc.relation.ispartofseriesCS-TR-4733en
dc.relation.ispartofseriesUMIACSen
dc.relation.ispartofseriesUMIACS-TR-2005-40en
dc.titleStable Factorizations of Symmetric Tridiagonal and Triadic Matricesen
dc.typeTechnical Reporten

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