Large Scale Sparse Singular Value Computations

In this paper, we present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly emphasize Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left-and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reeection tomography. The target architectures for our implementations of such methods are the Cray-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications in which approximate pseudo-inverses of large sparse Jacobian matrices are needed. It is hoped that this research will advance the development of future out-of-core sparse SVD methods, which can be used, for example, to handle extremely large sparse matrices (O(10 6) rows or columns) associated with extremely large databases in query-based information retrieval applications.