PERTURBATION ANALYSIS OF THE CHOLESKY DOWNDATING AND QR UPDATING PROBLEMS
1995 (English)In: Siam Journal on Matrix Analysis and Applications, Vol. 16, no 3, 760-775 p.Article in journal (Refereed) Published
Given upper triangular matrices R, G and column vectors x, f such that R(T)R - xx(T) and (R + G)(T)(R + G) - (x + f)(x + f)(T) are positive definite, let U and U + T be the corresponding Cholesky factors. In this paper, upper bounds on parallel to T parallel to in terms of parallel to G parallel to and parallel to f parallel to and upper bounds on parallel to T parallel to/parallel to U parallel to in terms of parallel to G parallel to/parallel to R parallel to and parallel to f parallel to/parallel to x parallel to are given, and the first order perturbation expansions of parallel to T parallel to and parallel to T parallel to/parallel to U parallel to are derived. Moreover, a perturbation analysis of the QR updating problem is also given.
Place, publisher, year, edition, pages
1995. Vol. 16, no 3, 760-775 p.
IdentifiersURN: urn:nbn:se:umu:diva-21994ISBN: 0895-4798OAI: oai:DiVA.org:umu-21994DiVA: diva2:212258