(University of Berg, 1999) Baryamureeba, Venansius; Steihaug, Trond; Zhan, Yin
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