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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.
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.