An implicitly restarted block Lanczos bidiagonalization method using Leja shifts
Document Type
Article
Date of Original Version
6-1-2013
Abstract
In this paper, we propose an implicitly restarted block Lanczos bidiagonalization (IRBLB) method for computing a few extreme or interior singular values and associated right and left singular vectors of a large matrix A. Our method combines the advantages of a block routine, implicit shifting, and the application of Leja points as shifts in the accelerating polynomial. The method neither requires factorization of A nor of a matrix that contains A. This makes the method well suited for very large matrices. For many matrices, the method presented in this paper requires less computational work and computer storage than other available approaches. Computed examples illustrate the performance of the method described. © 2012 Springer Science+Business Media Dordrecht.
Publication Title, e.g., Journal
BIT Numerical Mathematics
Volume
53
Issue
2
Citation/Publisher Attribution
Baglama, James, and Lothar Reichel. "An implicitly restarted block Lanczos bidiagonalization method using Leja shifts." BIT Numerical Mathematics 53, 2 (2013): 285-310. doi: 10.1007/s10543-012-0409-x.