Sequential randomized matrix factorization

Matrix factorization techniques play a key role in numerous data analysis and scientific computing tasks. This work extends recent research which uses randomized algorithms for performing matrix factorization.We develop and analyze a randomized method for incremental matrix factorization under certain uniform low-rankedness assumption. The main objective of this paper is to make the case for sequential randomized algorithms for approximate matrix factorizations of very large scale matrices. Numerical results and rigorous analysis of error bounds within a formal framework for the proposed sequential randomized algorithms are also outlined.