## 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

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.

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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