As one of the basic problems in matrix computation, rank-revealing has a wide variety of applications in scientific computing. Although the 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. This book presents a new rank-revealing algorithm for low rank matrices with efficient and reliable updating/downdating capabilities. The algorithm can provide a fast approach to find a low rank approximation to a data matrix, which plays a critical role in many applications. Interesting applications on information retrieval and image processing are also presented. The algorithms and applications in the book are useful to the community in scientific computing.

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