Improved Gram-Schmidt type downdating methods

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dc.contributor.authorBarlow, Jesse L.
dc.contributor.authorSmoktunowicz, Alicja
dc.contributor.authorErbay, Hasan
dc.date.accessioned2020-06-25T17:40:34Z
dc.date.available2020-06-25T17:40:34Z
dc.date.issued2005
dc.departmentKırıkkale Üniversitesi
dc.descriptionErbay, Hasan/0000-0002-7555-541X
dc.description.abstractThe problem of deleting a row from a Q-R factorization (called downdating) using Gram-Schmidt orthogonalization is intimately connected to using classical iterative methods to solve a least squares problem with the orthogonal factor as the coefficient matrix. Past approaches to downdating have focused upon accurate computation of the residual of that least squares problem, then finding a unit vector in the direction of the residual that becomes a new column for the orthogonal factor. It is also important to compute the solution vector of the related least squares problem accurately, as that vector must be used in the downdating process to maintain good backward error in the new factorization. Using this observation, new algorithms are proposed. One of the new algorithms proposed is a modification of one due to Yoo and Park [BIT, 36:161-181, 1996]. That algorithm is shown to be a Gram-Schmidt procedure. Also presented are new results that bound the loss of orthogonality after downdating. An error analysis shows that the proposed algorithms' behavior in floating point arithmetic is close to their behavior in exact arithmetic. Experiments show that the changes proposed in this paper can have a dramatic impact upon the accuracy of the downdated Q-R decomposition.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1007/s10543-005-0015-2
dc.identifier.endpage285en_US
dc.identifier.issn0006-3835
dc.identifier.issn1572-9125
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-27144496091
dc.identifier.scopusqualityQ2
dc.identifier.startpage259en_US
dc.identifier.urihttps://doi.org/10.1007/s10543-005-0015-2
dc.identifier.urihttps://hdl.handle.net/20.500.12587/3488
dc.identifier.volume45en_US
dc.identifier.wosWOS:000232663400003
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringeren_US
dc.relation.ispartofBit Numerical Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectorthogonalizationen_US
dc.subjectQ-R factorizationen_US
dc.subjectmatrix splittingsen_US
dc.subjectresidualen_US
dc.titleImproved Gram-Schmidt type downdating methodsen_US
dc.typeArticle

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