Article

Numerical Algorithms

, Volume 13, Issue 1, pp 123-152

First online:

Approximating dominant singular triplets of large sparse matrices via modified moments

  • Sowmini VaradhanAffiliated withDepartment of Computer Science, University of Tennessee
  • , Michael W. BerryAffiliated withDepartment of Computer Science, University of Tennessee
  • , Gene H. GolubAffiliated withDepartment of Computer Science, Stanford University

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Abstract

A procedure for 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 modified 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 modified 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 modified moments in conjunction with the Chebyshev semi-iterative method and deflation 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.

Keywords

Chebyshev semi-iterative method modified moments singular value decomposition sparse matrices

AMS subject classification

65K15 65K50 68P20