(joint with T.Y. Li (Michigan State University)
and Zhonggang Zeng (Northeastern Illinois University)
Rank-revealing has a wide range of applications in scientic computing such as
numerical polynomial algebra, signal processing and information retrieval.
Although singular value decomposition is the standard rank-revealing method,
it is costly in both computing time and storage when the ranks or the
nullities are low for large matrices, and it is inefficient in updating
and downdating when rows and columns are inserted or deleted.
Following up on a recent rank-revealing algorithm by T.Y. Li and Z. Zeng in
the low nullity case, we propose a new rank-revealing algorithm for low rank
matrices with efficient and reliable updating/downdating capabilities.
A comprehensive computing result shows the new method is accurate, robust,
and substantially faster than the existing rank-revealing algorithms.
Applications in image processing and information retrieval will be presented
in this talk.