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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References

SHOWING 1-10 OF 37 REFERENCES
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
  • 3,687
  • PDF
A robust incomplete factorization preconditioner for positive definite matrices
  • M. Benzi, M. Tuma
  • Mathematics, Computer Science
  • Numer. Linear Algebra Appl.
  • 2003
  • 102
  • PDF
MIQR: A Multilevel Incomplete QR Preconditioner for Large Sparse Least-Squares Problems
  • N. Li, Y. Saad
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 2006
  • 27
  • PDF
Direct methods for sparse linear systems
  • T. Davis
  • Computer Science
  • Fundamentals of algorithms
  • 2006
  • 1,248
Iterative methods for sparse linear systems
  • Y. Saad
  • Computer Science, Mathematics
  • 2003
  • 11,468
  • PDF
...
1
2
3
4
...