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One of the most important orthogonal decompositions from
numerical linear algebra is the
singular value decomposition (or SVD). This decomposition can
be used to solve both constrained and unconstrained
linear least squares problems, to perform matrix
rank estimation, and to estimate coefficients in canonical correlation
analysis. In scientific computing, the SVD is used in a wide
range of applications from information retrieval to seismic reflection
tomography [3]. Given extremely large and sparse
(unstructured) matrices, it is desirable to compute either a partial
or complete SVD in a fast and efficient way. Implementations which
exploit parallel processing on not only
multiprocessor environments but also on networks of high-performance
workstations are very of particular interest. Before discussing
candidate SVD algorithms for consideration, a few
fundamental characterizations of the SVD are outlined below.

Michael W. Berry (berry@cs.utk.edu)

Sun May 19 11:34:27 EDT 1996