Large sparse least squares computations

dc.contributor.author Ostrouchov, George
dc.contributor.department Statistics
dc.date 2018-08-16T15:43:51.000
dc.date.accessioned 2020-07-02T06:05:24Z
dc.date.available 2020-07-02T06:05:24Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 1984
dc.date.issued 1984
dc.description.abstract <p>Orthogonal Givens factorization is a popular method for solving large sparse least squares problems. Row and column permutations of the data matrix are necessary to preserve sparsity, and reduce the computational effort during factorization. The computation of a solution is usually divided into a symbolic ordering phase, and a numerical factorization and solution phase. Some theoretical results on row ordering are obtained using a graph-theoretic representation. These results provide a basis for a symbolic Givens factorization. Column orderings are also discussed, and an efficient algorithm for the symbolic ordering phase is developed. Sometimes, due to sparsity considerations, it is advantageous to leave out some rows from the factorization, and then update only the solution with these rows. A method for updating the solution with additional rows or constraints is extended to rank-deficient problems. Finally, the application of sparse matrix methods to large unbalanced analysis of variance problems is discussed. Some of the developed algorithms are programmed and tested.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/8204/
dc.identifier.articleid 9203
dc.identifier.contextkey 6330808
dc.identifier.doi https://doi.org/10.31274/rtd-180813-6855
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/8204
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/81167
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/8204/r_8505858.pdf|||Sat Jan 15 02:08:22 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Statistics
dc.title Large sparse least squares computations
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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