An implicitly restarted bidiagonal Lanczos Method forLarge-scale singular value problems

摘要

Low rank approximation of large and/or sparse rectangular matrices is a very import ant topic in many application problems and is closely related to the sin- gular value decomposition of the matrices. In this paper, we propose an implicit restart scheme for the bidiagonal Lanczos algorithm to compute a subset of the dominating singular triplets. We also illustrate the connection of the method with inverse eigenvalue problems. In the Lanczos process, we use the so-called one-sided reorthogonalization strategy to maintain the orthogonality level of the Lanczos vec- tors. The efficiency and the applicability of our algorithm are illustrated by some numerical examples from information retrieval applications.