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 method based on the Lanczos bidiagonalization and the Krylov–Schur method is presented. It is shown that deflation strategies can be easily implemented in this method and possible stopping criteria are discussed. Numerical experiments show the efficiency of the Krylov–Schur method.