LU Preconditioning for Overdetermined Sparse Least Squares Problems

@inproceedings{Howell2015LUPF,
  title={LU Preconditioning for Overdetermined Sparse Least Squares Problems},
  author={G. Howell and M. Baboulin},
  booktitle={PPAM},
  year={2015}
}
We investigate how to use an LU factorization with the classical lsqr routine for solving overdetermined sparse least squares problems. Usually L is much better conditioned than A and iterating with L instead of A results in faster convergence. When a runtime test indicates that L is not sufficiently well-conditioned, a partial orthogonalization of L accelerates the convergence. Numerical experiments illustrate the good behavior of our algorithm in terms of storage and convergence. 
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