A rank-revealing method for low rank matrices with updating, downdating, and applications.

摘要

As one of the basic problems in matrix computation, rank-revealing has a wide variety of applications in scientific computing. Although singular value decomposition is the standard rank-revealing method, it is costly in both computing time and storage when the rank or the nullity is low, and it is inefficient in updating and downdating when rows and columns are inserted or deleted. Consequently, alternative methods are in demand in those situations. Following up on a recent rank-revealing algorithm by Li and Zeng in the low nullity case, we present a new rank-revealing algorithm for low rank matrices with efficient and reliable updating/downdating capabilities. A comprehensive computing experiment shows the new method is accurate, robust, and substantially faster than existing rank-revealing algorithms.