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1. Introduction

  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 (
Sun May 19 11:34:27 EDT 1996