Approximating Dominant Singular Triplets of LargeSparse Matrices via Modi ed Moments

A procedure for determining determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modiied moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. Although no obvious relationship between modiied moments and the corresponding eigenvectors is known to exist, a scheme to approximate both eigenvalues and eigenvectors (and subsequently singular values and singular vectors) has been produced. This scheme exploits both modiied moments in conjunction with the Chebyshev semi-iterative method and deeation techniques to produce approximate eigenpairs of the equivalent sparse eigensystems. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations and a 256-processor Cray T3D is presented.