We present an efficient algorithm for computing a few extreme singular values of a large sparse m×n matrix C. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for CTC. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.
The first author is supported in part by NSF under Grant DMS-1317424. The second author is supported in part by NSF under Grant DMS-1317424 and DMS-1318633.
Liang, Qiao and Ye, Qiang, "Computing Singular Values of Large Matrices with an Inverse-Free Preconditioned Krylov Subspace Method" (2014). Mathematics Faculty Publications. 16.