An augmented LSQR method

Authors:
J. Baglama;L. Reichel;D. Richmond
Affiliations:
Department of Mathematics, University of Rhode Island, Kingston, USA 02881;Department of Mathematical Sciences, Kent State University, Kent, USA 44242;Department of Mathematics, University of Rhode Island, Kingston, USA 02881
Venue:
Numerical Algorithms
Year:
2013

Citing 13
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Abstract

The LSQR iterative method for solving least-squares problems may require many iterations to determine an approximate solution with desired accuracy. This often depends on the fact that singular vector components of the solution associated with small singular values of the matrix require many iterations to be determined. Augmentation of Krylov subspaces with harmonic Ritz vectors often makes it possible to determine the singular vectors associated with small singular values with fewer iterations than without augmentation. This paper describes how Krylov subspaces generated by the LSQR iterative method can be conveniently augmented with harmonic Ritz vectors. Computed examples illustrate the competitiveness of the augmented LSQR method proposed.