Approximating dominant singular triplets of large sparse matrices via modified moments

Sowmini Varadhan; Michael W. Berry; Gene H. Golub

doi:10.1007/bf02143130

Approximating dominant singular triplets of large sparse matrices via modified moments

Numerical Algorithms ◽

10.1007/bf02143130 ◽

1996 ◽

Vol 13 (1) ◽

pp. 123-152 ◽

Cited By ~ 4

Author(s):

Sowmini Varadhan ◽

Michael W. Berry ◽

Gene H. Golub

Keyword(s):

Sparse Matrices ◽

Modified Moments ◽

Large Sparse Matrices

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Estimating the largest singular values of large sparse matrices via modified moments

Numerical Algorithms ◽

10.1007/bf02142380 ◽

1991 ◽

Vol 1 (3) ◽

pp. 353-373 ◽

Cited By ~ 4

Author(s):

Michael Berry ◽

Gene Golub

Keyword(s):

Sparse Matrices ◽

Singular Values ◽

Modified Moments ◽

Large Sparse Matrices

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An Efficient Parallel Algorithm for Extreme Eigenvalues of Sparse Nonsymmetric Matrices

The International Journal of Supercomputing Applications ◽

10.1177/109434209200600106 ◽

1992 ◽

Vol 6 (1) ◽

pp. 98-111 ◽

Cited By ~ 2

Author(s):

S. K. Kim ◽

A. T. Chrortopoulos

Keyword(s):

Shared Memory ◽

Message Passing ◽

Sparse Matrices ◽

Data Locality ◽

Main Memory ◽

Global Memory ◽

Global Communication ◽

Step Method ◽

Arnoldi Algorithm ◽

Large Sparse Matrices

Main memory accesses for shared-memory systems or global communications (synchronizations) in message passing systems decrease the computation speed. In this paper, the standard Arnoldi algorithm for approximating a small number of eigenvalues, with largest (or smallest) real parts for nonsymmetric large sparse matrices, is restructured so that only one synchronization point is required; that is, one global communication in a message passing distributed-memory machine or one global memory sweep in a shared-memory machine per each iteration is required. We also introduce an s-step Arnoldi method for finding a few eigenvalues of nonsymmetric large sparse matrices. This method generates reduction matrices that are similar to those generated by the standard method. One iteration of the s-step Arnoldi algorithm corresponds to s iterations of the standard Arnoldi algorithm. The s-step method has improved data locality, minimized global communication, and superior parallel properties. These algorithms are implemented on a 64-node NCUBE/7 Hypercube and a CRAY-2, and performance results are presented.

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