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    On the Error in QR Integration

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    VanVleck_SIAMNA_46(3)1166.pdf (275.6Kb)
    Issue Date
    2008-03-07
    Author
    Dieci, Luca
    Van Vleck, Erik S.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    An important change of variables for a linear time varying system $\dot x=A(t)x, t\ge 0$, is that induced by the QR-factorization of the underlying fundamental matrix solution: $X=QR$, with Q orthogonal and R upper triangular (with positive diagonal). To find this change of variable, one needs to solve a nonlinear matrix differential equation for Q. Practically, this means finding a numerical approximation to Q by using some appropriate discretization scheme, whereby one attempts to control the local error during the integration. Our contribution in this work is to obtain global error bounds for the numerically computed Q. These bounds depend on the local error tolerance used to integrate for Q, and on structural properties of the problem itself, but not on the length of the interval over which we integrate. This is particularly important, since—in principle—Q may need to be found on the half-line $t\ge 0$.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/06067818X.
    URI
    http://hdl.handle.net/1808/17247
    DOI
    https://doi.org/10.1137/06067818X
    Collections
    • Mathematics Scholarly Works [255]
    Citation
    Dieci, Luca & Van Vleck, Erik. "On the Error in QR Integration." (2008) SIAM J. Numer. Anal., 46(3), 1166–1189. (24 pages). http://dx.doi.org/10.1137/06067818X.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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