Document Type
Article
Date of Original Version
10-2013
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.
Citation/Publisher Attribution
Baglama, J., Reichel, L., & Richmond, D. Numer Algor (2013). 64:263. doi: 10.1007/s11075-012-9665-8
Available at: http://dx.doi.org/10.1007/s11075-012-9665-8
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