Properties of a class of preconditioners
for weighted least squares problems
Venansius Baryamureeba, Trond Steihaug and Yin Zhang
A sequence of weighted linear least squares problems arises from
interior-point methods for linear programming where the changes from
one problem to the next are the weights and the right hand side. One
approach for solving such a weighted linear least squares problem is
to apply a preconditioned conjugate gradient method to the normal
equations where the preconditioner is based on a low-rank correction
to the Cholesky factorization of a previous coefficient matrix. In
this paper, we establish theoretical results for such preconditioners
that provide guidelines for the construction of preconditioners of
this kind. We also present preliminary numerical experiments to
validate our theoretical results and to demonstrate the effectiveness
of this approach.
Technical Report No. 170,
Department of Informatics, University of Bergen,
N-5020 Bergen, Norway and
Technical Report No. TR99-16,
Department of Computational and Applied Mathematics,
Rice University, Houston, Texas 77005, USA.
April 30, 1999 (Revised July 6, 1999)
Contact: [email protected]
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