Sparsity analysis of the QR factorization

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dc.contributor.authorHare, D.
dc.contributor.authorJohnson, C. R.
dc.contributor.authorOlesky, D. D.
dc.contributor.authorVan den Driessche, P.
dc.date.accessioned2010-05-05T19:59:12Z
dc.date.available2010-05-05T19:59:12Z
dc.date.copyright1991en
dc.date.issued2010-05-05T19:59:12Z
dc.descriptionOriginally published March 1990. Revised November 1991.en
dc.description.abstractGiven only the zero-nonzero pattern of an m-by-n matrix A of full column rank, which entries of Q and which entries of R in its QR factorization must be zero and which entries may be nonzero? We give a complete answer to this question, which involves an interesting interplay between combinatorial structure and the algebra implicit in orthogonality. To this end some new sparse structural concepts are introduced, and an algorithm to determine the structure of Q is given. The structure of R then follows immediately from that of Q and A. The computable zero/nonzero structures for the matrices Q and R are proven to be tight, and the conditions on the pattern for A are the weakest possible (namely that it allows matrices A with full column rank). This complements existing work that focussed upon R and then only under an additional combinatorial assumption (the strong Hall property).en
dc.description.sponsorshipNSF grant DMS90-00839, Office of Naval Research Contract N00014-90-J-1739, NSERC Grants A-8214, A-8965 and the University of Victoria Committee on Faculty Research and Travelen
dc.identifier.urihttp://hdl.handle.net/1828/2709
dc.language.isoenen
dc.relation.ispartofseriesDMS-536-IRen
dc.subjectQR factorizationen
dc.subjectbipartite graphen
dc.subjectHall propertyen
dc.subjectsparse matrixen
dc.subjectcombinatorial matrix theoryen
dc.subjectorthogonalityen
dc.titleSparsity analysis of the QR factorizationen
dc.typeTechnical Reporten

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