Qiang Ye
Computing Singular Values of Large Matrices with an Inverse Free Preconditioned Krylov Subspace Method

Department of Mathematics
University of Kentucky
Lexington
KY 40506-0027
qye3@uky.edu
Qiao Liang

We present an efficient algorithm for computing a few extreme (largest and smallest) singular values and corresponding singular vectors of a large sparse $m\times n$ matrix $C$ . Our algorithm is based on reformulation of the singular value problem as an eigenvalue problem for $C^T C$ and, to address the clustering of singular values, we use 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 such as deflations. Numerical tests will be presented to demonstrate efficiency and robustness of the new algorithm.