V-invariant methods for generalised least squares problems

M. R. Osborne

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    An important consideration in solving generalised least squares problems is the dimension of the covariance matrix V. This has the dimension of the data set and is large when the data set is large. In addition the problem can be formulated to have a well determined solution in cases where V is illconditioned or singular, a class of problems that includes the case of equality constrained least squares. This paper considers a class of methods which factorize the design matrix A while leaving V invariant, and which can be expected to be well behaved exactly when the original problem solution is well behaved. Implementation is most satisfactory when V is diagonal. This can be achieved by a preprocessing step in which V is replaced by the diagonal matrix D which results from the modified Cholesky factorization PVPT → LDLT where L is unit lower triangular and P is the permutation matrix associated with diagonal pivoting. Conditions under which this replacement is satisfactory are investigated.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    EditorsPeter M.A. Sloot, David Abramson, Alexander V. Bogdanov, Yuriy E. Gorbachev, Jack J. Dongarra, Albert Y. Zomaya
    Place of PublicationBerlin
    PublisherSpringer Verlag
    Pages673-682
    Number of pages10
    EditionPeer Reviewed
    ISBN (Print)9783540401964
    DOIs
    Publication statusPublished - 2003
    EventInternational Conference on Computational Science (ICCS 2003) - Melbourne Australia and St Petersburg Russia (joint)
    Duration: 1 Jan 2003 → …

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2659
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    ConferenceInternational Conference on Computational Science (ICCS 2003)
    Period1/01/03 → …
    OtherJune 2 2003

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