A Krylov-Schur approach to the truncated SVD

Abstract

Computing a small number of singular values is required in many practical applications and it is therefore desirable to have efficient and robust methods that can generate such truncated singular value decompositions. A new method based on the Lanczos bidiagonalization and the Krylov-Schur method is presented. It is shown how deflation strategies can be easily implemented in this method and possible stopping criteria are discussed. Numerical experiments show that existing methods can be outperformed on a number of real world examples.